MINE  GASES  AND  VENTILATION 


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MINE  GASES  AND  VENTILATION 

TEXTBOOK  FOR  STUDENTS  OF  MINING,  MINING 

ENGINEERS  AND  CANDIDATES  PREPARING 

FOR  MINING  EXAMINATIONS 

Designed  for  Working  Out  the  Various  Problems  That 

Arise  in  the  Practice  of  Coal  Mining,  as  They  Relate 

to  the  Safe  and  Efficient  Operation  of  Mines 


BY 
JAMES  T.  BEARD,  C.E.,  E.M. 

SENIOR  ASSOCIATE  KDITOB,  COAL  AGE;  FORMERLY  PRINCIPAL  SCHOOL  OF  MINES,  INTER- 
NATIONAL CORRESPONDENCE  SCHOOLS,  AND  ASSOCIATE  EDITOR  MINES  AND  MINER- 
ALS, 8CRANTON,  PA.;  PROFESSOR  OF  CHEMISTRY,  SCHOOL  OF  THE  LACKAWANNA ; 
SECRETARY  STATE  BOARD  OF  MINE  EXAMINERS,  IOWA;  MEMBER  AMERICAN  INSTITUTE 
MINING  ENGINEERS;  INSTITUTION  OF  MINING  ENGINEERS,  ENGLAND;  MINE  INSPEC- 
TORS' INSTITUTE  OF  AMERICA;  FELLOW  AMERICAN  ASSOCIATION  FOR  THE  ADVANCE- 
MENT OF  SCIENCE. 


SECON.O  EDITION 
REVISED*  AND  ENT,ARGFI> 


McGRAW-HILL  BOOK  COMPANY,  INC. 

NEW  YORK:    239   WEST  39TH  STREET 

LONDON:    6  &  8  BOUVERIE  ST.,  E.  C.  4 

1920 


T/V  3  0V 


COPYRIGHT,  1916,  192J 

BY 

JAMES  T.  BEARD 


TMK  MAPLE  PRESS  YORK  PA 


PREFACE  TO  SECOND  EDITION 

Any  one  who  has  been  closely  associated  with  the  practi- 
cal operation  of  coal  mines  will  realize  quickly  the  need  of 
technical  knowledge  relating  to  the  safe  and  economical 
production  of  coal.  In  no  department  of  the  work  is  this 
need  more  urgent  than  in  the  ventilation  of  the  mine. 

A  knowledge  of  the  properties  and  behavior  of'  the  gases 
found  or  generated  in  the  mine,  and  the  means  for  effecting 
their  safe  removal  or  rendering  them  harmless  are  of  chief 
importance,  requiring  careful  study  combined  with  practical 
experience  in  the  operation  of  mines. 

Experience,  without  a  knowledge  of  the  theory  of  mining,  is 
little  better  than  is  the  possession  of  such  knowledge  by 
one  who  has  had  no  experience  in  the  practical  work.  Ex- 
perience and  knowledge  must  go  hand  in  hand. 

The  problems  relating  air,  gases,  ventilation,  safety  lamps, 
breathing  apparatus,  rescue  work,  gas  and  dust  explosions 
in  mines  are  treated  in  a  thoroughly  practical  manner,  while 
at  the  same  time  showing  their  correct  solution.  Formulas 
must  always  play  an  important  part  in  mine  ventilation  and 
their  treatment  is  made  as  simple  as  possible. 

No  effort  has  been  spared  to  make  this  volume  a  standard 
of  ventilating  practice.  With  this  end  in  view,  the  various 
constants  used  have  been  carefully  selected  and  are  those 
most  generally  adopted.  Particularly  is  this  true  of  the 
tables  of  weight  and  measures  and  the  conversion  tables 
relating  to  the  common  and  metric  systems  given  in  the 
Addenda.  Their  use  is  recommended. 

The  present  volume,  which  replaces  the  little  booklet  issued 
by  Coal  Age,  some  time  previous,  under  the  same  title,  will  be 
recognized  as  a  second  edition  of  that  handbook,  though  greatly 
enlarged  by  the  addition  of  whole  new  sections  on  Safety 
Lamps,  Oils,  Breathing  Apparatus,  Rescue  Work  and  numer- 
ous tables,  making  it  a  complete  treatise  on  the  subject.  The 
author  desires  to  thank  those  who  have  generously  lent  their 

vii 


\  tr  <i  : 


viii  PREFACE 

aid  in  the  work,  among  whom  he  would  particularly  mention 
James  W.  Paul,  Mining  Engineer,  Federal  Bureau  of  Mines, 
and  J.  T.  Ryan,  Vice-president  and  General  Manager,  Mine 
Safety  Appliances  Co.,  Pittsburgh,  Pa. 

JAMES  T.  BEARD. 
NEW  YORK  CITY, 
June,  1920. 


PREFACE  TO  FIRST  EDITION 

In  March,  1913,  there  was  started  in  Coal  Age  a  depart- 
ment entitled  "  Study  Course  in  Coal  Mining,"  and  each 
week  following  that  date  there  have  appeared  two  pages  of 
matter  in  pocket-book  form,  which  were  intended  to  be  later 
compiled  and  published  as  "The  Coal  Age  Pocket  Book." 

The  publication  of  these  weekly  pages  was  not  confined 
to  a  consecutive  order,  which  gave  to  that  department  of 
Coal  Age  an  increasing  and  widening  interest  among  readers 
and  students  of  technical  mining  subjects.  The  matter 
treated  was  in  response  to  the  requests  of  coal-mining  men, 
who  were  seeking  to  know  the  development  of  formulas,  the 
explanation  of  principles,  and  the  most  approved  and  gener- 
ally adopted  methods  in  the  practice  of  coal  mining.  The 
requests  that  have  been  received  from  publishers  of  similar 
technical  matter,  asking  for  the  privilege  of  reproducing  many 
of  the  pages  already  published  in  Coal  Age,  is  sufficient  evid- 
ence of  the  technical  value  of  the  work. 

Recently,  so  many  letters  have  come  from  mining  men 
and  from  several  mining  classes  who  have  been  studying  the 
pages  as  they  have  appeared  each  week,  asking  that  the 
matter  already  prepared  be  published  at  once  in  suitable  book 
form,  it  has  been  decided  to  issue  the  following  sections  on 
the  atmosphere,  gases  and  ventilation  of  mines.  Although  it 
is  not  assumed  that  these  sections  are  in  their  final  form,  they 
contain  much  valuable  matter  that  will  be  appreciated  by 
practical  mining  men  and  students  of  coal  mining. 

Coal  Age  particularly  commends  this  work  to  mining 
students,  engineers,  mine  foremen,  assistant  foremen  and 
firebosses,  superintendents  and  managers.  The  book  con- 
tains only  original  matter,  prepared  at  great  expense  of  time 
and  labor,  involving  much  careful  research  and  experiment. 
The  author  does  not  hesitate  to  say  that  many  of  the  practical 
problems  in  the  ventilation  of  mines,  which  cannot  be  solved 

ix 


x  PREFACE 

by  the  usual  methods  employed,  are  easily  worked  by  the 
potential  methods  explained  fully  in  these  pages.  No  mine 
official  or  mine  employee  can  afford  to  be  without  this  edition 
in  his  reference  file  or  library. 

JAMES  T.  BEARD. 
NEW  YORK  CITY, 
July,  1916. 


CONTENTS 

PAGE 
CHAPTER  I 

Am -.        1 

The  atmosphere — The  barometer — Physics  of  air  and  gases — 
Matter — Measurement — Density  and  volume — Specific  gravity 
—Occlusion,  emission,  diffusion  of  gases. 

CHAPTER  II 

HKAT 42 

Sources  and  measurement  of  heat — Chemistry  of  gases — 
Thermochemistry — Hygrometry — Steam. 

CHAPTER  III 

MINE  GASES 86 

Geological  conditions — Common  mine  gases — Hydrocarbon 
gases — Properties  and  behavior  of  mine  gases — Methane — 
Firedamp — Carbon  monoxide — Carbon  dioxide — Blackdamp — 
Afterdamp — Inflammable  and  explosive  mine  gases. 

CHAPTER  IV 

EXPLOSIONS  IN  MINES 116 

Definition,  gas  explosion,  dust  explosion — Inflammation  of  gas 
— Nature  and  temperature  of  flame — Explosion  of  gas — Coal 
dust,  its  inflammability  and  influence;  effect  of  stone  dust — 
Mine  explosion,  development,  causes,  mixed  lights,  electric 
mine  lamps,  prevention  of  mine  explosions. 

CHAPTER  V 

MINE  RESCUE  WORK  AND  APPLIANCES 131 

Preliminary,  entering  a  mine  after  explosion,  first-aid  sugges- 
tions— Breathing  apparatus,  principle,  action  and  requirements 
in  respiration,  development,  design  and  testing  of  breathing 
apparatus — Types  of  breathing  apparatus,  Draeger,  Fleuss 
Proto,  Gibbs,  Paul — Bureau  of  Mines,  permissible  breathing 
apparatus — Specifications  by  the  Bureau  of  Mines — First-aid 
work. 

CHAPTER  VI 

THEORY  OF  VENTILATION 161 

Mine  ventilation — Problems — Flow  of  air  in  airways — Ventil- 
ating pressure,  how  produced  and  measured,  the  water  gage — 
Velocity  of  air  currents — Quantity  of  air,  requirements — Work 
or  power  on  the  air — Equivalents  in  measurement — Examples 

xi 


xii  CONTENTS 

for  practice — -Mine  airways — Symbols  and  formulas — Mine 
potential  methods — Measurement  •  of  air  currents — Examples 
for  practice — Tandem  circulations — Splitting  the  air  current — 
Natural  division  of  air — Examples  in  natural  division — 'Pro- 
portionate division  of  air,  kinds  of  regulators — Secondary  split- 
ting—Theoretical considerations  in  splitting — Practical  problem. 

CHAPTER  VII 

PRACTICAL  VENTILATION 248 

Conducting  air  currents,  air  bridges — General  plan  of  mine — 
Distribution  of  air  in  the  mine — Splitting  air  currents — Sys- 
tems of  ventilation — Systems  of  mine  airways. 

CHAPTER  VIII 

MINE  LAMPS  AND  LIGHTING 26$ 

Principles  of  construction — Safety  lamps,  classification  and 
requirements — Characteristic  types  of  lamps — Special  types  of 
safety  lamps — Permissible  mine  safety  lamps — Use  and  care  of 
safety  lamps — Testing  for  gas  by  indicators — The  flame  test — 
Illuminants  for  safety  lamps,  oils,  etc. — Miner's  carbide  lamps — 
Electric  mine  lamps — Permissible  portable  electric  mine  lamps. 

ADDENDA 328 

Logarithms — Circular  functions,  sines  and  cosines,  tangents 
and  cotangents — Squares,  cubes,  roots  and  reciprocals  of  num- 
bers— Circumferences  and  areas — Denominate  numbers — 
Weights  and  meaures — United  States  and  British  systems — 
Metric  systems  of  weights  and  measures — Conversion  tables 
— Conversion  of  compound  units. 

INDEX  .  .415 


MINE  GASES  AND  VENTILATION 


SECTION  I 
AIR 

THE  ATMOSPHERE — THE  BAROMETER — PHYSICS  OF  AIR  AND 
GASES — MATTER — MEASUREMENT — DENSITY  AND  VOL- 
UME— SPECIFIC  GRAVITY — OCCLUSION,  EMISSION,  DIFFU- 
SION OF  GASES 

Little  was  known  of  the  aerial  envelope  that  surrounds  the 
earth,  until  the  researches  of  Cavendish  and  Priestley  in  Eng- 
land and  Lavoisier  in  France,  in  the  latter  part  of  the  18th 
century  showed  that  air  was  not  an  element,  as  had  been 
supposed,  but  a  mechanical  mixture  of  gases. 

Up  to  this  time,  air  and  all  combustible  material  was  be- 
lieved to  contain  a  certain  substance  called  "phlogiston," 
which  escaped  as  flame  when  the  substance  was  burned. 
Both  Cavendish  and  Priestley  held  this  phlogistic  theory  even 
after  they  discovered  the  complex  nature  of  air.  Hence,  the 
name  " dephlogisticated  air"  was  applied  to  oxygen;  while 
hydrogen  was  called  "inflammable  air"  and  carbon  dioxide 
" fixed  air." 

It  remained  for  Lavoisier  to  expose  this  fallacy  by  showing 
that  no  matter  was  lost,  but  the  .weight  of  the  products  of  a 
combustion  was  equal  to  that  of  the  combustibles  burned. 
A  large  number  of  carefully  made  analyses  showed  a  prac- 
tically constant  proportion  of  the  two  chief  gases  of  which 
air  is  formed.  This  seemed  to  suggest  that  the  oxygen  and 
nitrogen  of  the  air  were  chemically  united,  although  the  pro- 
portion of  each  gas  did  not  correspond  to  its  combining  power 

1 


2  MINE  GASES  AND  VENTILATION 

as  determined  by  the5  Analyses  of  well-known  chemical  com- 
pounds. The  character  of  air  as  a  mechanical  mixture  thus 
became  definitely  established. 

Besides  the  two  principal  gases  oxygen  and  nitrogen  that 
constitute-  the  air  we  breathe,  there  are  other  gases  whose 
presence  in  the  atmosphere  is  of  much  vital  importance, 
although  their  proportion  is  small.  Of  these  may  be  men- 
tioned carbon  dioxide,  water  vapor,  ammonia,  argon  and 
ozone. 

Carbon  dioxide  is  most  important,  because  of  its  toxic  effect 
on  the  human  system.  This  effect,  it  is  stated  on  the  highest 
authority,  increases  with  the  barometric  pressure.  Thus,  for 
example,  air  containing  but  1  per  cent,  carbon  dioxide,  at  a 
pressure  of  4,  5  or  6  atmospheres  produces  the  same  effect  on 
the  respiratory  organs  as  air  containing  4,  5  or  6  per  cent,  of 
the  gas  at  a  pressure  of  1  atmosphere.  In  other  words,  the 
true  gage  of  the  effect  of  this  gas  in  inspired  air  is  the  percentage 
of  the  gas  multiplied  by  the  number  of  atmospheres. 

Water  vapor  present  in  the  atmosphere  breathed  has  a 
marked  effect  on  the  vital  activities  and  the  consequent  de- 
velopment of  physical  energy  in  the  body.  In  what  manner 
the  relative  humidity  of  the  inspired  air  operates  to  impair 
the  physical  force  has  not  been  fully  explained;  but  experience 
has  shown  that  a  high  degree  of  humidity  in  a  warm  atmos- 
phere or  climate  has  an  extremely  weakening  effect  on  the 
human  system. 

The  association  of  high  humidity  and  temperature  marks  a 
comparatively  large  amount  of  water  per  unit  volume  of  air 
and,  to  that  extent,  it  may  be  assumed  impairs  the  respiratory 
functions  of  the  lungs.  The  result  is  to  incapacitate  men 
exposed  to  such  conditions  and  render  them  wholly  or  in  part 
unfit  to  perform  the  required  manual  or  mental  labor.  These 
effects  are  continually  observed  in  the  warm  moist  atmosphere 
of  deep  mine  workings  and  other  similar  places. 

The  Respiratory  System. — Respiration  is  the  prime  means 
of  maintaining  the  vital  action  in  animal  organisms.  Its 
objects  are  twofold:  1.  The  oxidation  of  the  organic  matter 
of  the  animal  tissues  with  the  resulting  development  of  vital 


AIR  3 

energy.  2.  The  removal  of  the  carbon  dioxide  produced  in 
the  process  of  oxidation.  Both  of  these  processes  are  per- 
formed through  the  medium  of  the  blood. 

The  Circulation. — Under  the  action  of  the  respiratory  sys- 
tem, the  blood  flows  from  the  heart  into  and  through  the 
arteries  of  the  body,  as  water  flows  through  a  circulating 
pipe  system  under  the  action  of  a  pump.  The  pulsations  of 
the  heart,  corresponding  to  the  strokes  of  the  pump,  force  the 
blood  through  a  complex  system  of  arteries  and  veins  to  every 
portion  of  the  body  and  limbs. 

All  the  blood  does  not  flow  in  a  continuous  circuit,  but  the 
arteries  branch,  forming  separate  channels  leading  to  different 
parts  of  the  body.  The  time  required  to  complete  a  circuit  and 
return  to  the  heart  is  obviously  widely  different,  varying  from 
20  or  30  sec.  to  one-fourth  as  many  minutes.  This  is  of  in- 
terest in  relation  to  the  time  required  for  poison  entering  the 
blood  to  be  disseminated  throughout  the  system. 

Respiratory  Action. — The  action  known  as  " breathing" 
originates,  or,  at  least,  is  regulated  by  a  nerve  center  at  the 
base  of  the  brain  from  which  impulses  are  transmitted  through 
the  spinal  column  to  the  respiratory  muscles.  By  this  means 
air  enters  the  air  cells  of  the  lungs  and  oxygen,  absorbed  there- 
from by  the  red  corpuscles  (haemoglobin)  of  the  blood,  is 
carried  by  the  circulation  to  the  tissues  of  the  body,  where  it  is 
consumed  with  the  production  of  carbon  dioxide.  This  gas 
is  absorbed  by  the  blood  and  carried  back  through  the-veins  to 
the  heart  and  lungs,  where  it  gives  up  a  portion  of  its  gas, 
which  enters  the  lungs  and  is  expelled  by  each  succeeding 
exhalation. 

While  air  expired  by  a  healthy  adult,  at  rest,  contains  from 
2  to  3  per  cent,  carbon  dioxide,  careful  determinations  show  a 
constant  production  of  5.6  per  cent,  of  this  gas  in  the  lungs 
when  the  person  is  at  rest. 

Quantity  of  Oxygen  Consumed  in  Breathing. — A  man  at  rest 
consumes  263  cm.3  of  oxygen  per  min.,  or  263  X  0.06102  =  16 
cu.  in.  per  min.  and  exhales  an  equal  volume  of  carbon  dioxide. 
Air  exhaled  from  the  lungs  contains  2.6  per  cent,  carbon 
dioxide,  18.3  per  cent,  oxygen,  79.1  per  cent,  nitrogen.  In  vio- 


4  MINE  GASES  AND  VENTILATION 

lent  exercise,  a  man  consumes  from  eight  to  nine  times  the 
amount  of  oxygen  required  when  at  rest;  or,  say  128  to  144 
cu.  in.  per  min.  The  exhaled  breath  may  then  contain  6.6  per 
cent,  carbon  dioxide  and  only  14.3  per  cent,  oxygen. 

Depletion  of  Oxygen  in  Air,  Effect  on  Life. — Air  containing 
3  per  cent,  carbon  dioxide  can  be  breathed  without  discomfort, 
even  when  the  oxygen  content  has  been  reduced  to  16  per 
cent.;  but  5  per  cent,  carbon  dioxide  causes  headache,  dizzi- 
ness and  nausea,  after  a  short  time.  When  no  carbon  dioxide 
is  present  in  the  air  the  oxygen  content  may  fall  as  low  as 
14  per  cent,  before  much  difficulty  is  experienced  in  breathing; 
but  air  containing  but  10  per  cent,  is  no  longer  breathable; 
but  will  cause  death  quickly  by  suffocation. 

Composition  of  Air. — Normal  air  is  composed  chiefly  of 
oxygen  and  nitrogen,  which  are  invariably  mixed  in  the  fol- 
lowing proportions  expressed  as  percentage  by  volume  and 
by  weight  of  each  of  these  gases : 

TABLE  SHOWING  COMPOSITION  OF  NORMAL  AIR 

By  Volume  By  Weight 

Oxygen 20 . 9  per  cent.  23 . 0  per  cent. 

Nitrogen 79 . 1  per  cent.  77 . 0  per  cent.  ' 


100 . 0  per  cent.  100 . 0  per  cent. 

Air  also  contains  0.04  per  cent,  of  carbon  dioxide  (CO2), 
together  with  smaller  amounts  of  argon,  ammonia  and  water 
vapor.  Atmospheric  air,  it  may  be  said,  is  never  absolutely 
dry  or  free  of  moisture.  The  term  "dry  air"  in  respect  to  the 
atmosphere  is  only  a  relative  expression,  meaning  that  such 
air  is  comparatively  dry. 

Weight  of  Dry  Air. — The  weight  of  dry  air,  per  unit  volume, 
varies  directly  with  the  pressure  it  supports,  and  inversely 
as  its  absolute  temperature.  There  are  two  formulas  for 
finding  the  weight  of  1  cu.  ft.  of  air,  one  being  expressed  in 
terms  of  the  barometer  (B),  in  inches,  and  the  other  in  terms 
of  the  pressure  (p)  in  pounds  per  square  inch. 

1.3273  B 

By  the  barometer,  w  - 


By  the  pressure,  w 


0.37  (460  +  «) 


AIR  5 

Moisture  in  Air. — This  subject  is  fully  treated  under 
"Hygrometry,"  and  it  is  sufficient  here  to  say  that  the  water 
absorbed  or  held  by  the  air  is  an  invisible  vapor  that  resem- 
bles a  gas  in  its  behavior,  until  a  sufficient  amount  is  present 
to  fully  saturate  the  space  it  occupies.  This  point  of  satura- 
tion is  called  the  "dew  point,"  because  at  that  point  any  excess 
of  vapor  condenses  and  appears  as  a  mist  or  cloud.  The  con- 
densation is  more  rapid  in  contact  with  a  cold  surface. 

Normal  Air. — The  term  " normal  air"  in  respect  tb  its  com- 
position refers  to  air  containing  a  normal  percentage  of 
oxygen  (20.9  per  cent.)  as  given  above.  When  the  percentage 
of  oxygen  present  is  less  than  normal  the  air  is  said  to  be 
" depleted"  of  its  oxygen.  This  frequently  occurs  in  poorly 
ventilated  places  in  mines.  The  depletion  of  oxygen  is  the 
result  of  the  various  forms  of  combustion  or  oxidation  that 
are  constantly  taking  place  in  mines,  and  is  also  caused  by 
the  absorption  of  oxygen  from  the  air  by  the  coal. 

Mine  Air. — Except  when  diluted  with  other  gases,  the  air 
I'n  a  well-ventilated  mine  never  shows  any  appreciable  deple- 
tion of  its  oxygen  content.  Even  in  poorly  ventilated  places 
it  is  exceptional  to  find  less  than  20  per  cent,  of  oxygen  ex- 
cept where  other  gases  are  being  generated  in  considerable 
volume  whereby  the  air  is  diluted  and  the  percentage  of 
oxygen  correspondingly  diminished.  This  fact  has  been  well 
established  by  innumerable  tests  of  mine  air  made  at  different 
mines  and  under  varying  conditions  of  ventilation. 

THE  ATMOSPHERE 

The  atmosphere  is  the  aerial  envelope  surrounding  the 
earth.  The  term  is  also  used  to  describe  the  air  or  gaseous 
mixture  filling  any  given  space;  as,  for  example,  the  mine 
atmosphere  is  the  air  and  gases  filling  the  mine  or  any  por- 
tion of  the  workings. 

Atmospheric  Pressure. — The  weight  of  the  air  surrounding 
the  earth  causes  a  pressure,  which  decreases  as  the  height 
above  the  surface  increases;  and  the  density  of  the  air  de- 
creases in  like  manner,  with  the  elevation  above  sea  level. 


6  MINE  GASES  AND  VENTILATION 

Variation  of  Atmospheric  Pressure. — Atmospheric  pressure 
at  any  given  place  varies  irregularly  with  the  condition  in 
respect  to  storms;  the  storm  center  being  always  an  area  of 
lower  pressure  than  that  surrounding  the  storm.  In  this 
country,  a  variation  of  2  in.  of  mercury  (say  1  Ib.  per  sq.  in.) 
in  atmospheric  pressure,  in  48  hr.,  is  not  uncommon. 

There  is  also  a  regular  daily  variation,  the  pressure  at- 
taining a  maximum  about  10  o'clock  and  a  minimum  at  4 
o'clock,  morning  and  evening.  There  is,  likewise,  a  yearly 
variation,  the  general  pressure  reaching  a  maximum,  in  the 
northern  hemisphere,  in  January  and  a  minimum  in  July. 

THE  BAROMETER 

The  Mercurial  Barometer. — The  pressure  of  the  atmosphere 
is  measured  by  the  height  of  mercury  column  it  will  support 
against  a  vacuum.  The  mercurial  barometer  is  a  glass  tube, 
about  36  in.  long,  closed  at  one  end.  This  is  first  filled  with 
mercury  and  then  inverted.  The  open  end  being  immersed  in 
a  basin  of  the  same  liquid,  the  mercury  in  the  tube  will  fall  to 
a  height  above  the  surface  .of  that  in  the  basin,  such  that 
the  pressure  of  the  atmosphere  acting  on  the  surface  of  the 
liquid  in  the  basin  will  support  the  mercury  column  in  the 
tube. 

Barometric  Pressure. — The  pressure  of  the  atmosphere  ex- 
pressed in  inches  of  mercury  is  called  the  barometric  pres- 
sure. For  example,  at  sea  level,  the  atmospheric  pressure 
will  commonly  support  30  in.  of  mercury  column;  or  is  equiva- 
lent to  a  barometric  pressure  of  30  in. 

Calculation  of  Barometric  Pressure. — One  cubic  inch  of 
mercury  (32°F.)  weighs  0.49  Ib.  A  barometric  pressure  of 
30  in.,  therefore,  indicates  an  atmospheric  pressure  of 

0.49  X  30  =  14.7  Ib.  per  sq.  in. 

which  is  the  normal  pressure  at  sea  level. 

Calculation  of  Water  Column. — The  height  of  water  col- 
umn, in  feet,  the  atmospheric  pressure  will  support  is  found 
by  multiplying  the  pressure  (Ib.  per  sq.  in.)  by  2.3;  or  dividing 
the  same  by  0.434.  Or  the  barometric  pressure,  in  inches, 


AIR 


multiplied   by  one  and  one-eighth  will  give  the  equivalent 
water  column,  in  feet.     For  example,  at  sea  level, 
14.7  X  2.3  =  33.8,  say  34  ft. 
30  X  1>6  =  33.75,  say  34  ft. 

Principle  of  the  Barometer. — In  the  mercurial  barometer 
the  pressure  of  the  atmosphere  supports  the  column  of  mercury 
in  the  tube.  The  weight  of  the  atmosphere  counterbalances 
the  weight  of  the  mercury 
column,  which  rises  as  the 
atmospheric  pressure  increases 
and  falls  as  it  decreases.  The 
height  of  the  mercury  column 
is  therefore  a  true  index  of  the 
pressure  of  the  atmosphere  at 
the  surface  of  the  earth,  at  the 
moment  of  taking  the 
observation. 

The  principle  of  the  balance 
pressure  between  the  air  and 
the  mercury  is  clearly  illus- 
trated in  Fig.  1,  where  a  glass 
tube)  closed  at  one  end,  is 
shown  supported  in  a  basin  of 
mercury.  The  surface  of  the 
liquid  in  the  basin  is  shown  as 
divided  into  imaginary  squares,  by  lines  one  inch  apart;  and 
the  small  arrow-heads  represent  the  pressure  of  the  atmosphere 
exerted  on  each  square  inch  of  surface. 

Suppose  for  a  moment,  that  the  column  of  mercury  in 
the  tube  is  exactly  one  square  inch  in  cross-section;  it  is  evident, 
in  that  case,  that  the  mercury  column  takes  the  place  of  the 
atmospheric  pressure  on  one  square  inch  of  surface;  and, 
since  there  is  perfect  equilibrium,  its  weight  is  equal  to  the 
pressure  of  the  atmosphere  per  square  inch. 

Furthermore,  whatever  the  sectional  area  of  the  mercury 
column,  it  is  clear  that  its  weight  will  always  equal  the  atmos- 
pheric pressure  for  the  same  area  of  surface.  Hence,  the 
area  of  mercury  column  is  not  important,  but  its  height  only. 


FIG.  l. 


8  MINE  GASES  AND  VENTILATION 

If  the  weight  of  one  cubic  inch  of  mercury  (0.4911  Ib.) 
be  multiplied  by  the  observed  height  of  the  column  of  mercury 
measured  in  inches,  the  product  will  be  the  pressure  of  the 
atmosphere,  in  pounds  per  square  inch,  at  the  place  where  the 
observation  was  taken.  This  assumes,  that  the  barometric 
reading  has  been  reduced  to  a  standard  reading,  at  a  tem- 
perature of  32  deg.  (Fahr.),  which  must  be  done  when  mak- 
ing accurate  determinations. 

Standard  Barometric  Readings. — Owing  to  the  fact  that 
the  mercury  in  the  tube  expands  and  contracts  more  rapidly 
than  the  glass  of  the  tube,  the  reading  of  the  barometer  will 
vary  slightly  for  the  same  pressure,  at  different  temperatures. 

In  comparing  barometric  readings  taken  at  different  times 
and  at  varying  temperatures,  it  is  necessary  to  carefully 
note  the  temperature  when  the  reading  was  taken  and  reduce 
the  observed  reading  to  a  so-called  standard  reading  at  32 
deg.  F. 

Calling  the  standard  reading  H,  the  observed  reading  h  and 
the  temperature  t  (Fahr.),  the  corrected  reading  is  found  by 
the  formula, 

H  =  h(l  -  0.0002  0 

For  example,  the  standard  reading  corresponding  to  30  in. 
of  barometer,  observed  at  a  temperature  of  60  deg.  is 

30  (1  -  0.0002  X  60)  =  29.64  in. 

It  is  even  possible,  owing  to  the  more  rapid  expansion  or 
contraction  of  the  mercury  than  of  the  glass,  that  an  observed 
fall  of  barometer  may  correspond  to  an  actual  rise  in  atmos- 
pheric pressure,  or  vice  versa,  within  about  0.4  in. 

Description  of  the  Instrument. — In  the  illustration,  Fig.  2, 
is  shown  the  common  form  of  the  standard  mercurial  barom- 
eter. The  glass  tube  that  contains  the  mercury  column  is 
here  inclosed  in  the  metal  case  A,  to  the  bottom  of  which  is 
attached  a  somewhat  larger  casing  B.  The  latter  holds  a 
glass  cylinder  G  terminated  at  the  bottom  with  a  chamois- 
skin  bag,  the  whole  forming  the  basin  that  holds  the  mercury. 

The  entire  case  AB  is  hung  in  a  truly  vertical  position,  sup- 
ported on  a  substantial  base;  as  shown  in  the  figure.  The  top 


AIR 


of  the  mercury  column  is  observed  through  the  opening  O, 
in  the  upper  end  of  the  case.  In  this  opening,  is  arranged  a 
sliding  vernier  V,  which  can  be  adjusted,  by  means  of  the 
thumbscrew  D,  so  that  its  lower  edge  exactly  corresponds  with 
the  top  of  the  mercury  column.  The  position  of  the  vernier 
is  then  read  on  the  scale  S  marked  on  the  sides  of  the  opening 
in  the  case.  This  scale  is  graduated  in 
inches,  but  only  extends  an  inch  or  two 
above  and  an  equal  distance  below  the 
normal  barometric  reading.  The  normal 
reading  at  sea  level  is  about  30  in.,  and 
the  scale  extends  from  26  to  32  inches. 

Before  setting  the  vernier,  however,  it  is 
necessary  to  adjust  the  level  of  the  mercury 
in  the  basin  so  that  it  corresponds  exactly 
with  what  would  be  the  zero  of  the  ex- 
tended scale.  To  enable  this  to  be  done 
with  precision,  there  is  attached  to  the 
scale  a  long  rod  that  extends  downward 
inside  the  casing.  The  lower  end  of  the 
rod  is  drawn  to  a  fine  point  that  marks 
the  zero  of  the  scale. 

To  adjust  the  level  of  the  mercury  in  the 
basin,  the  thumb-screw  C  is  turned.  This 
screw  bears  against  the  bottom  of  the 
chamois-skin  bag  and  operates  to  raise  or 
lower  the  level  of  the  surface  of  the  mer- 
cury in  the  glass  cylinder.  The  adjustment 
is  complete  when  the.  fine  pointed  end  of 
the  rod  is  seen  to  just  prick  the  surface  of 
the  mercury.  The  point  of  the  rod  is  observed  through  the 
glass  cylinder  above  the  surface  of  the  mercury. 

A  thermometer  T  is  shown  attached  to  the  metal  case.  In 
making  accurate  observations  it  is  necessary  to  reduce  all 
readings  to  standard  readings. 

The  Aneroid  Barometer.  —  The  aneroid  barometer  consists 
of  a  metallic  case,  having  a  flexible  vacuum  box  within,  which 
is  sensitive  to  the  slightest  change  in  atmospheric  pressure. 


FlG  2. 


10  MINP  GASES  AND  VENTILATION 

The  corrugated  diaphragm  forming  the  back  of  the  vacuum 
box  is  supported  against  the  pressure  of  the  atmosphere  by  a 
steel  spring,  and  its  movement  under  changes  of  pressure  is 
communicated  to  the  index  hand  or  needle  that  registers 
the  pressure  on  a  dial  calibrated  to  read  inches  of  mercury 
corresponding  to  the  readings  of  the  mercurial  barometer 
under  the  same  pressures  (Fig.  3). 


FIG.  3. 

The  aneroid  being  portable  is  very  useful  in  ascertaining 
quickly  differences  in  elevation  of  two  or  more  points  in 
mines  and  on  the  surface.  The  dial  of  mining  aneroids  has 
two  concentric  scales.  The  inner  scale  of  the  aneroid  shown 
in  the  accompanying  figure  is  graduated  to  read  inches  of 
mercury,  while  the  outer  scale  reads  feet  of  elevation.  It 
has  always  been  the  custom,  in  arranging  the  graduation  of 
these  two  scales,  to  make  the  altitude  scale  read 


AIR 


11 


TABLE   SHOWING    ATMOSPHERIC    PRESSURE    AT    DIFFERENT 

ELEVATIONS  AND  CORRESPONDING  DENSITY  OF  AIR 

FOR  DIFFERENT  TEMPERATURES 


"-  eg 

ii 

•8|2 

»ll 
&** 

c 
*o  . 

II 
& 

e 

go, 

If 

f 

!? 

n 

Temperature  (deg.  F.) 

-20 

0 

32 

60 

100 

200 

300 

400 

Weight  of  dry  air  (Ib.  per  cu.  ft.) 

25,000 

11.343 

5.571 

0.0 

0342 

.0327 

.0306 

.0290 

.0269 

'.0228 

.0198 

.0175 

20,000 

13.874 

6.814 

8.0 

0418 

.0400 

.0373 

.0354 

.0329 

.0279 

.0242 

.0214 

15,000 

16.948 

8.323 

17.0 

0511 

.0489 

.0457 

.0433 

.0402 

.0341 

.0296 

0262 

14,000 

17.626 

8.656 

18.8 

0532 

.0509 

.0475 

.0450 

.0418 

.0354 

.0308 

.0272 

13,000 

18.328 

9.000 

20.7 

0553 

.0529 

.0494 

.0468 

.0434 

.0369 

.0320 

.0283 

12,000 

19  053 

9.357 

22.7 

0575 

.0550 

.0514 

.0486 

.0452 

.0383 

.0333 

.0294 

11,000 

19  805 

9.726 

24.8 

0597 

.0571 

'.0534 

.0505 

.0469 

.0398 

.0346 

.0306 

10,000 

20.582 

0.107 

27.0 

0621 

.0594 

.0555 

.0525 

.0488 

.0414 

.0359 

.0318 

9,000 

21  .392 

0.505 

29.4 

0645 

.0617 

.0577 

.0546 

.0507 

.0430 

.0374 

.0330 

8,000 

22  229 

0.916 

32.0 

0670 

.0641 

.0600 

.0567 

.0527 

.0447 

.0388 

.0343 

7,000 

23.088 

11.339 

34.8 

.0696 

.0666 

.0623 

.0589 

.0547 

.0464 

.0403 

.0356 

6,000 

23.975 

11.774 

37.8 

.0723 

.0692 

.0647 

.0612 

.0568 

.0482 

.0419 

.0370 

5,000 

24.890 

12.224 

41.0 

.0751 

.0718 

.0671 

.0635 

.0590 

.0500 

.0435 

.0384 

4,500 

25.360 

12.455 

42.7 

.0765 

.0732 

.0684 

.0647 

.0601 

.0510 

.0443 

.0391 

4,000 

25.837 

12.689 

44.4 

.0779 

.0745 

.0697 

.0659 

.0612 

.0520 

.0451 

.0399 

3.500 

26.322 

12.927 

46.2 

.0794 

.0759 

.0710 

.0672 

.0624 

.0529 

.0460 

.0406 

3,000 

26.813 

13.169 

48.0 

.0809 

.0774 

.0723 

.0684 

.0635 

.0539 

.0468 

.0414 

2,500 

27.315 

13.415 

49.9 

.0824 

.0788 

.0737 

.0697 

.0647 

0549 

.0477 

.0422 

2,000 

27.824 

13.665 

51.8 

.0839 

.0803 

.0751 

.0710 

.0659 

.0559 

.0486 

.0429 

1,500 

28.339 

13.918 

53.8 

.0855 

.0818 

.0764 

.0723 

.0672 

.0570 

.0495 

.0437 

1,000 

28.861 

14.174 

55.8 

.0871 

.0833 

.0778 

.0737 

.0684 

.0580 

.0504 

.0445 

900 

28.966 

14.225 

56.1 

.0874 

.0836 

.0781 

.0739 

.0686 

.0582 

.0506 

.0447 

800 

29.072 

14.277 

56.4 

.0877 

.0839 

.0784 

.0742 

.0689 

.0585 

.0508 

.0449 

700 

29.178 

14.329 

56.7 

.0880 

.0842 

.0787 

.0745 

.0691 

.0587 

.0510 

.0450 

600 

29.296 

14.387 

57.0 

.0884 

.0845 

.0790 

.0748 

.0694 

.0589 

.0512 

.0452 

500 

29.390 

14.433 

57.4 

.0886 

.0848 

.0793 

.0750 

.0696 

.0591 

.0513 

.0454 

400 

29  .496 

14  .486 

57.8 

.0890 

.0851 

.0796 

.0753 

.0699 

.0593 

.0515 

.0455 

300 

29  603 

14.538 

58.3 

.0893 

.0854 

.0799 

.0756 

.0702 

.0595 

.0517 

.0457 

200 

29.710 

14.591 

58.8 

.0896 

.0857 

.0801 

.0758 

.0704 

.0597 

.0519 

.0458 

100 

29.818 

14.643 

59.4 

.0899 

.0860 

.0804 

.0761 

.0707 

.0600 

.0521 

.0460 

Seal 
level/0 

29.925 

14.696 

60.0 

.0903 

.0863 

.0807 

.0764 

.0709 

.0602 

.0523 

.0462 

-500 

30.469 

14  .963 

.0919 

.0879 

.0822 

.0778 

0722 

.0613 

.0532 

.0470 

-  1,000 

31  .022 

15.235 

.0936 

.0895 

.0837 

.0792 

.0735 

.0624 

.0542 

.0479 

-  1,500 

31.582 

15.510 

.0953 

.0911 

.0852 

.0806 

.0749 

.0635 

.0552 

.0487 

-  2,000 

32.1-51 

15.789 

0970 

.0928 

.0867 

.0821 

.0762 

.0647 

.0561 

.0496 

-  2,500 

32.727 

16.072 

.0987 

.0944 

.0883 

.0835 

.0776 

.0658 

.0572 

.0505 

-3,000 

33.312 

16.359 

.1005 

.0961 

.0899 

.0850 

.0790 

.0670 

.0582 

.0514 

-  3,500 

33  .903 

16.650 

.1023 

.0978 

.0915 

.0865 

.0804 

.0682 

.0592 

.0523 

-  4,000 

34.504 

16.945 

.1041 

.0996 

.0931 

.0881 

.0818 

.0694 

.0603 

.0533 

-4,500 

35.113 

17.244 

.1059 

.1013 

.0947 

.0896 

.0832 

.0706 

.0613 

.0542 

-  5,000 

35  73C 

17.547 

.1078 

.1031 

.0964 

.0912 

.0847 

.0719 

.0624 

.0551 

12 


MINE  GASES  AND  VENTILATION 


The  table  on  the  preceding  page  is  deduced  from  the  de- 
terminations of  atmospheric  density  and  pressure,  under  nor- 
mal conditions,  at  different  elevations  above  and  below  sea 
level,  as  established  by  the  celebrated  British  astronomer 
royal,  Sir  George  Biddle  Airy  (1840),  and  the  aeronautic  ob- 
servations of  Herschel  and  Glaisher. 

The  atmospheric  pressures  in  the  third  column  of  the  table 
are  the  mean  of  many  direct  observations  taken  at  different 
altitudes,  under  normal  conditions,  and  constitute  what  are 
generally  known  as  "Airy's  tables." 

The  temperatures  in  the  fourth  column  correspond  to  the 
mean  observed  temperatures,  -at  different  altitudes  and  are 
based  on  a  sea-level  temperature  of  60  deg.  F.  They  are  sug- 
gestive of  the  rate  of  cooling  or  fall  of  temperature  with  re- 
spect to  increase  of  altitude. 

The  following  table  shows  the  mean  observed  temperatures 
of  the  atmosphere  at  different  altitudes,  the  rate  of  fall  (deg. 
per  1000  ft.)  and  the  estimated  average  temperature  of  air 
column  extending  from  sea  level  to  each  respective  altitude 
given : 

TABLE    SHOWING    RELATION   OF    MEAN    TEMPERATURE   TO  ALTITUDE, 
IN  THE  ATMOSPHERE 


Altitude  or  elevation 
above  sea  level,  ft. 

1 
Mean  observed 
temperature, 
deg.  F. 

Rate  of  fall  in 
temperature, 
deg.  per  1000  ft. 

Mean  average 
temperature  of  air 
column,  deg.  F. 

25,000 

0 

1.6 

24 

20,000 

8 

1.8 

29 

15,000 

17 

2.0 

35 

10,000 

27 

2.5 

42 

8,000 

32 

3.0 

45 

5,000 

41 

3.5 

50 

3,000 

48 

4.0 

54 

0 

60 

The  mean  average  temperature  of  air  column  extending 
from  sea  level  to  any  altitude  given  in  the  above  table  makes 
it  possible  to  calculate  the  normal  barometric  pressure  for 
that  altitude,  by  means  of  the  following  formula : 


AIR  13 

The  application  of  this  formula  requires  the  use  of  a  table  of 
seven-place  logarithms  or  more.  It  serves  to  check  the  tem- 
perature observations  at  these  altitudes. 

Bh  =  29.926[l  ±  ^~m]k 
in  which 

Bh  =  barometric  pressure,  at  altitude  h  (in.)  ; 
T  =  average  absolute  temperature  of  air  column,  ex- 

tending from  sea  level  to  altitude  h  (deg.  F.); 
h  =  altitude  above  sea  level  (ft.). 

The  sign  ±  ,  in  the  formula,  relates  to  the  altitude  h,  as 
being  above  or  below  sea  level.  For  altitudes  above  sea 
level,  the  second  term  within  the  brackets  is  negative  and  the 
minus  (  —  )  sign  must  be  used.  For  altitudes  below  sea  level, 
this  term  is  positive  and  the  plus  (+)  sign  is  employed. 

Relation  of  Drop  in  Temperature  to  Altitude.  —  Approxi- 
mately, the  fall  in  temperature  (t),  in  the  atmosphere,  varies 
as  the  1.4  root  of  the  height  (h)  above  the  sea  level;  thus, 


Applying  this  principle  and  assuming  a  temperature  drop 
of  6  deg.  at  an  altitude  of  1000  ft.  above  sea  level,  disregard- 
ing the  effect  of  the  radiation  of  heat  from  the  earth,  the 
mean  average  temperature  (/),  for  any  altitude  (h),  expressed 
in  thousands  of  feet,  can  be  calculated  approximately  thus  : 


This  formula  assumes  a  normal  sea-level  temperature  of  60 
deg.  F.,  which  is  the  first  term  in  the  second  member  of  the 
equation.  The  second  term  of  this  member  accounts  for  the 
fall  of  temperature  corresponding  to  the  increase  of  altitude; 
while  the  third  term  expresses  the  effect  of  the  radiation  of 
heat  from  the  earth,  which  varies  inversely  as  the  square  of 
the  altitude  factor  h  —  2,  probably  owing  to  the  influence  of 
clouds  or  vapor  in  the  lower  atmosphere. 

Example.  —  Let  it  be  required  to  find  the  temperature,  at  an  elevation 
of  8000  ft.  above  sea  level,  corresponding  to  a  normal  temperature  of 
60  deg.  at  sea  level. 


14  MINE  GASES  AND  VENTILATION 

Solution.  —  In  this  case,  the  altitude  expressed  in  thousands  of  feet  is 
h  =  8  ;  which  substituted  in  the  formula  gives  : 

t  =  60  -  6     '^8  +  (8-^2)2  =  33.4  deg.  F. 

The  mean  observed  temperature  for  this  altitude  as  given  in  the  table  is 
32  deg.  F. 

Average  Temperature  of  Air  Column.  —  The  average  tem- 
perature of  the  air  column  extending  from  sea  level  to  any 
altitude  h,  expressed  in  thousands  of  feet,  can  be  calculated 
with  close  approximation  by  the  formula 

1.28  /  — 

Average  temp.  =  60  —  3  \/h 

The  mean  average  air-column  temperature,  as  calculated  by 
this  formula,  can  be  used  to  find  the  corresponding  normal 
atmospheric  pressure  by  substituting  its  value,  reduced  to  ab- 
solute temperature  (T),  in  the  formula 


The  use  of  this  formula  will  require  a  table  of  seven-place 
logarithms  or  more.  In  the  solution  of  the  following  example, 
a  ten-place  logarithmic  table  was  employed. 

Example.  —  Find  the  mean  average  air-column  temperature  correspond- 
ing to  a  sea-level  temperature  of  60  deg.  F.,  for  an  elevation  of  12,000  ft. 
above  the  sea. 

Solution.  —  In  this  case,  h  =  12,  which  gives  for  the  mean  average  air- 
column  temperature 

Average  temp.  =  60  -  3^/12  =  39  deg.  F. 

The  absolute  temperature  is  460  +   39  =   499  deg.F.,  abs. 

Example.  —  Calculate  the  normal  atmospheric  pressure  for  an  altitude 
of  12,000  ft.,  using  the  mean  average  air-column  temperature  found  in 
the  last  example,  T  =  499  deg.  F.  abs. 

Solution.  —  Substituting  the  given  values  in  the  formula  gives  for  the 
normal  atmospheric  pressure  at  this  altitude, 

Pi2.ooo  =  14.696  (l  -  53  28^  499)  ^  '°°  =  9-359  lb-  Per  scl-  in- 

The  diagram  shown  on  the  following  page  compiles  the 
data  relating  to  average  observed  temperatures  at  different 
elevations,  and  the  calculated  heights  of  the  corresponding 


AIR 


15 


water  and  mercury  columns,  weight  and  pressure  of  air,  of 
interest  to  the  student  of  atmospheric  conditions. 


^              Atmospheric  Pressure^ 

1!  l! 

\. 

£ 

.c 

I 

if 

olumn(lnches> 

11   it 

11     |! 

£j">          ££ 

0      ;J 

Lb.  per  so. 

Lb.persq. 

Water  Co, 
Maximum  L 

Mercury  C 

25,000- 

yJS 

\ 
I 
I 

0" 

0.0327 

802.2 

5.571 

12.85 

11.343 

30,000- 

' 

1 

\ 

\ 

P" 

0.0393 

9812 

6.814 

15.70 

f  3.874 

15,000- 

(/) 

17° 

0.0472 

1198.5 

8.323 

19.17 

16.948 

k, 

]  0,000- 

c 
5 

27" 

0.0561 

1455.4 

10.107 

23.30 

20.582 

5POO- 

i 

41° 

0.0659 

1760.3 

12.224 

28.'dO 

24.890 

1,000- 
SeaLeveL 

-1. 

55' 
60" 

0.0744 
0,0764 

2041.1 
2116.2 

14.174 
14.696 

32.70 
33.90 

28JB61 
29.925 

The  Differential  Method. — The  pressure  of  the  atmosphere, 
per  unit  area,  at  any  altitude  x  is  due  to  the  weight  of  air 
column  above  such  point  of  observation.  Air  being  com- 
pressible, any  increment  of  pressure  (dp z),  causes  a  corre- 
sponding minus  increment  of  height  (—&x)',  and,  calling  the 
unit  weight  of  air  wx  at  the  altitude  x,  we  have 

8px  =  —wx5x  (1) 

But  the  unit  weight  of  air  varies  with  the  pressure  it  sup- 
ports. Hence,  calling  this  unit  weight  and  pressure  at  sea 


16  MINE  GASES  AND  VENTILATION 

level  WQ  and  po,  respectively,  and  that  at  any  altitude  x,  wx, 
and  px,  we  have 

Wx       px  W0 

—  =  —  ;  and  wx  =  ~px  (2) 

W0       Po  Po 

Substituting  this  value  in  equation  1  and  dividing  both  mem- 
bers of  the  equation  by  px,  gives 

&5--2U.  (3) 

Px  Po 

But,  the  differential  of  a  quantity  divided  by  the  quantity  is 
equal  to  the  differential  of  its  Naperian  logarithm. 

Hence,        5  log  p*  =  -  —  5X;  or  5X  =  -^°  d  log  px  (4) 

PO  ™o 

Then  integrating  between  the  limits  x  =  0,  and  x  =  h,  remem- 
bering that  when  x  =  0,  px  =  p0;  and  when  x  =  h,  px  =  p^ 
and  subtracting  the  lower  integral  from  the  higher, 

fc-0=£(logp0-logpft)  (5) 

Wo 

But  the  unit  weight  of  dry  air  at  sea  level,  normal  atmos- 
pheric pressure  (Ib.  per  sq.  ft.),  is 

(6) 


which,  substituted  in  equation  5,  gives  for  the  altitude  corre- 
sponding to  any  pressure,  under  normal  conditions, 

h  =  53.28T7  (log  po  -  log  Ph)  (7) 

Or,  expressed  in  common  logarithms, 

h  =  122.6877(log  po  -  log  Ph)  (8) 

For  normal  atmospheric  pressure,  at  sea  level,  po  =  14.696  Ib. 
per  sq.  in.,  and  log  14.696  =  1.1672;  hence 

h  =  122.68T  (1.1672  -  log  ph) 
Or,  log  ph  =  1.1672  -  (10) 


AIR  17 

PHYSICS  OF  AIR  AND  GASES 

The  volume  of  any  given  weight  of  air  or  gas  depends  on 
two  factors — the  temperature  of  the  gas  and  the  pressure  it 
supports. 

Effect  of  Temperature. — -For  any  given  weight  of  air  or  gas, 
its  volume  varies  directly  as  its  absolute  temperature,  as- 
suming the  pressure  remains  constant. 

Effect  of  Pressure. — For  any  given  weight  of  air  or  gas,  its 
volume  varies  inversely  as  the  pressure  it  supports,  assuming 
the  temperature  remains  constant. 

Expansion  and  Contraction  of  Air  or  Gas. — Any  change  in 
temperature  or  pressure  causes  a  corresponding  change  in  the 
volume  of  the  air  or  gas,  as  follows : 

Increase  of  temperature  causes  expansion. 

Decrease  of  temperature  causes  contraction. 

Increase  of  pressure  causes  contraction. 

Decrease  of  pressure  causes  expansion. 

Coefficient  of  Expansion  or  Contraction. — The  coefficient  of 
expansion  is  the  same  as  that  of  contraction.  This  coefficient 
relates  to  change  in  volume  due  to  change  in  temperature  and 
is  practically  the  same  for  all  gases  and  air  and  independent 
of  the  pressure. 

The  coefficient  of  expansion  of  air  or  gas  is  the  ratio  of 
the  increase  in  volume  to  the  original  volume,  for  an  increase 
of  one  degree  in  temperature.  Since  a  degree  of  the  Fahren- 
heit scale  is  %  of  a  degree  of  the  centigrade  scale,  it  is  evident 
that  the  Fahrenheit  coefficient  of  expansion  will  be  exactly 
%  of  the  centigrade  coefficient.  These  coefficients  are  as 
follows:  Centigrade,  0.003663;  Fahrenheit,  0.002035. 

Illustration. — Let  it  be  required  to  find  the  increase  in  volume  in  an  air 
current  of  100,000  cu.  ft.  entering  a  mine  at  a  temperature  of  32  deg.  F. 
and  discharged  at  a  temperature  of  68  deg.  F. 

Solution. — The   rise  in   temperature   is   68-32  =  36  deg.   F.     The 
increase  in  volume,  calculated  by  the  Fahrenheit  scale,  is 
100,000  X  0.002035  X  36  =  7326  cu.  ft. 

Or,  since  68  and  32  deg.  F.  correspond  to  20  and  0  deg.  C.,  the  rise 
in  temperature  is  20  —  0  =  20  deg.  C.,  and  the  increase  in  volume, 
calculated  by  the  centigrade  scale,  is 

100,000  X  0.003663  X  20  =  7326  cu.  ft. 


18  MINE  GASES  AND  VENTILATION 

Note.  —  Instead  of  multiplying  by  these  coefficients,  it  is 
possible  to  divide  by  their  reciprocals,  which  are 

Fahrenheit,  ^^  =  491.4,  say  492 

Centigrade,  ±        =  273 


These  numbers,  being  divisors,  show  that  air  or  gas  ex- 
pands or  contracts  H?3  of  its  volume,  for  each  degree  rise  or 
fall  in  temperature  (centigrade);  or  ^92  of  the  san.3  volume 
for  each  degree  rise  or  fall  in  temperature  (Fahrenheit)  .  The 
figures  point  to  what  has  been  called  the  "absolute  zero"  of 
temperature  scales  as  being  273  deg.  below  freezing  (  —  273°C.) 
or  492  deg.  below  freezing  (-460°F.). 

Absolute  Zero.  —  The  so-called  "absolute  zero"  of  tempera- 
ture scales  is  based  on  the  observed  rate  of  expansion  and 
contraction  of  all  gases  and  air.  This  rate  is  practically 
M?3  of  the  volume,  per  degree  centigrade;  or  3^92  of  the 
volume,  pier  degree  Fahrenheit.  It  is  clear  that  if  this  rate 
continued  unchanged  a  fall  in  temperature  of  273  deg.  C.,  or 
492  deg.  F.,  below  the  freezing  point  of  water,  would  reduce 
the  volume  of  the  gas  to  zero,  when  all  molecular  vibrations 
would  cease,  indicating  a  total  absence  of  heat  and  pressure. 

The  absolute  zero  has  therefore  been  fixed  at  273  deg.  below 
the  common  zero  of  the  centigrade  scale  (  —  273°C.),  which 
corresponds  to  460  deg.  below  zero  on  the  Fahrenheit  scale. 
The  fixing  of  this  point  is  purely  arbitrary,  its  chiel  value  being 
the  facility  it  affords  in  the  calculation  of  gaseous  volumes 
with  respect  to  temperature. 

Absolute  Temperature.  —  Absolute  temperatures  differ  from 
common  temperatures  only  in  being  estimated  from  the 
absolute  zero.  Hence  the  absolute  temperature  is  obtained 
from  the  common  temperature  by  adding  273  in  the  centi- 
grade or  460  in  the  Fahrenheit  scale;  thus, 

30  deg.  C.  =  273  +  30  =  303  deg.,  absolute. 
60  deg.  F.  =  460  +  60  =  520  deg.  absolute. 

Relation  of  Volume  and  Absolute  Temperature  of  Air  and 
Gas.  —  The  law  commonly  known  as  Gay  Lussac's  or  Charles' 


AIR 


10 


law  makes  the  volume  of  all  gases  and  air,  under  constant 
pressure,  vary  directly  as  the  absolute  temperature. 

This  relation  is  clearly  illustrated  in  Fig.  4,  which  assumes 
a  volume  of  460  cu.  ft.  of  air  or  gas  at  0  deg.  F.,  corresponding 
to  the  absolute  temperature  at  that  point.  It  will  be  ob- 
served that  this  volume  expands  and  contracts  exactly  as  the 
absolute  temperature  rises  or  falls, 
except  at  the  lowest  temperatures  £ 
approaching  the  liquefaction  of  the 
air  or  gas*  where  the  law  naturally 
fails,  owing  to  the  changing  state 
of  the  matter. 

Relation  of  Volume  and  Pressure 
of  Air  and  Gas. — For  a  constant 
temperature,  the  volume  of  air 
and  gases  varies  inversely  as  the 
pressure  supported.  In  this  con- 
nection, pressure  is  often  estimated 
as  one,  two,  three,  etc . ,  atmospheres, 
meaning  that  the  pressure  sup- 
ported by  the  air  or  gas  is  one, 
two,  three,  etc.,  times  the  normal 
atmospheric  pressure  at  that  place. 
This  is  commonly  known  as  Boyle's 
or  Mariotte's  law  of  volume. 

An  " atmosphere"  is  sometimes 
incorrectly  taken  to  mean  normal 
sea-level  pressure  (14.7  Ib.  per  sq. 
in.).  '  Such  a  meaning  of  the  term, 
however,  would  manifestly  limit 
its  application  to  sea  level,  or 
furnish  an  arbitrary  standard  inconvenient  for  use. 

The  term  "free  air"  relates  to  atmospheric  air  at  any 
elevation  and  for  any  condition.  According  to  the  above  rule, 
when  free  air  is  compressed  to  two,  three  or  four  atmospheres 
its  volume  is  reduced  to  J^,  %  or  Y±  of  the  original  volume, 
assuming  the  temperature  remains  constant.  At  the  same 
time,  the  pressure  or  tension  of  the  air  is  increased  to  two, 


60 


0-460 


AIR  LIQUEFIES 


\AB50LUTE  ZERO 
FIG.  4. 


20  MINE  GASES  AND  VENTILATION 

three  or  four  times  the  atmospheric  or  free-air  pressure,  what- 
ever that  may  have  been,  assuming  always  a  constant  tem- 
perature of  the  air. 

The  expansion  of  air,  by  the  same  law,  is  accompanied  by 
a  fall  of  pressure,  the  volume  ratio  being  equal  to  the  inverse 
pressure  ratio,  for  the  same  temperature.  The  pressure  re- 
ferred to  here  is  the  absolute  pressure,  or  the  pressure  above 
a  vacuum  or  zero. 

Relation  of  Absolute  Temperature  and  Pressure  of  Air  and 
Gas. — For  a  constant  volume,  the  absolute  temperature  of  air 
and  gases  varies  directly  as  the  absolute  pressure. 

Volume,  Temperature,  Pressure  of  Air  and  Gas. — The  rela- 
tion of  the  volume  (v),  pressure  (p)  and  absolute  temperature 
(T),  for  a  given  weight  of  air  or  gas  is  expressed  simply  by 
the  following  formulas : 

Constant  pressure  Constant  temperature  Constant  volume 

02    =    T*  Vz    =    pi  p2    =    Tz 

vi       Tl  vi       p2  pi    '  Ti 

The  relations  of  volume,  temperature  and  pressure  of  air 
and  gas  depend  on  two  main  conditions:  1.  The  gas  may  or 
may  not  be  free  to  expand.  2.  Heat  may  or  may  not  be  added 
or  taken  from  the  gas. 

Addition  of  Heat. — Two  cases  may  arise,  as  follows : 

(a)  If  the  air  is  confined  (constant  volume)  the  rise  in 
temperature  is  more  rapid,  since  all  the  heat  is  then  trans- 
formed into  heat  energy  or  internal  work,  and  the  pressure 
rises  accordingly. 

(6)  If  the  air  is  free  to  expand  (constant  pressure)  the 
rise  in  temperature,  for  the  same  addition  of  heat,  is  much 
less  rapid.  In  this  case,  the  air  in  expanding  performs  ex- 
ternal work  against  the  pressure  it  supports.  A  part  of  the 
heat  added  is  thus  absorbed  in  doing  outside  work  while  the  re- 
mainder, only,  is  available  for  internal  work  and  manifest 
as  heat  energy,  thus  causing  a  lesser  rise  of  temperature. 

Work  of  Expansion  of  Air. — When  air  is  expanded  by  the 
addition  of  heat  the  external  work  performed  can  be  calculated 
in  two  ways,  as  follows : 

1.  On  a  heat-unit  basis,  by  subtracting  the  heat  absorbed, 


AIR  21 

per  pound  of  air,  per  degree  rise  in  temperature,  for  constant 
volume,  from  the  heat,  per  pound,  per  degree,  for  constant 
pressure;  and  multiplying  this  difference,  which  is  the  heat 
converted  into  external  work,  by  the  foot-pounds  per  heat 
unit;  thus,  since  1  B.t.u.  =  778ft.-lb., 

Heat,  per  Ib.-deg.  (sp.  heat,  const,  pressure)  ............  0.2374  B.t.u. 

Heat,  per  Ib.-deg.  (sp.  heat,  const,  volume)  .............  0.  1689  B.t.u. 

Heat,  per  Ib.-deg.,  available  for  external  work  .........  0.0685  B.t.u. 

External  work,  per  Ib.-deg  .........  0.0685  X  778  =  53.29  ft.-lb. 

2.  The  external  work  performed  in  the  expansion  of  air,  per 
pound,  per  degree,  can  be  calculated,  also,  very  simply  by 
multiplying  the  volume  of  1  Ib.  of  dry  air,  at  1  deg.  F.,  abso- 
lute, and  1  Ib.  per  sq  .  in.  .pressure  (0.37  cu.  ft.),  by  144,  the 
number  of  square  inches  in  1  sq.  ft.  ;  thus, 
External  work,  per  Ib.-deg.  .  .  .  0.37  X  144  =  53.28  f  t.-lb. 

Adiabatic  Expansion  and  Compression.  —  When  there  is  no 
addition  of  heat  in  the  expansion,  or  no  loss  of  heat  in  the  com- 
pression of  air  or  gas,  the  relations  of  volume,  temperature 
and  pressure  follow  other  laws  than  those  previously  given. 
Such  expansion  or  compression  is  described  as  "adiabatic," 
meaning  no  passage  (of  heat)  in  or  out  of  the  gas. 

In  adiabatic  expansion,  there  being  no  addition  of  heat, 
the  increase  in  volume  is  at  the  expense  of  the  internal  en- 
ergy and  a  fall  of  temperature  is  the  result,  which  is  accom- 
panied also  by  a  fall  of  pressure. 

In  adiabatic  compression,  there  being  no  loss  of  heat,  the 
internal  energy  is  augmented  by  the  heat  of  compression,  and 
the  result  is  an  increase  of  both  temperature  and  pressure. 

Adiabatic  Formulas.  —  The  following  formulas  express  the 
relation  of  volume  (v)f  pressure  (p)  and  absolute  tempera- 
ture (T),  for  any  given  weight  of  air  or  gas,  when  expanded 
or  compressed  without  gain  or  loss  of  heat.  In  actual  prac- 
tice it  is  only  possible  to  approximate  adiabatic  expansion 
or  compression: 

7117  v*  =  /T\\  2-469  p,  =  (T,\  3- 

vi      \Tj  Pl      \Tj 


2=yj  . 
Pi      W 


^      /tM 
T,      W 


P?°'288 


22  MINE  GASES  AND  VENTILATION 

It  is  important  to  observe  that  adiabatic  expansion  or 
compression  always  involves  a  change  in  temperature.  Where 
the  temperature  is  maintained  constant,  by  adding  heat  in 
expanding,  or  extracting  heat  (cooling)  in  compressing,  the 
change  in  volume  is  described  as  "isothermal"  expansion 
or  compression.  In  practice,  it  is  only  possible  to  approximate 
isothermal  conditions  in  the  expansion  or  compression  of  air 
or  gas. 

The  application  of  the  above  formulas  necessitates  the  use 
of  logarithms. 

MATTER 

Definition. — Matter  is  the  tangible  substance  occupying 
space  and  endowed  with  properties  that  give  to  it  form,  motion 
and  other  distinguishing  characteristics,  by  virtue  of  an  all- 
pervading  or  impressed  subtle  force  generally  described  as 
electrical. 

Divisions  of  Matter. — Until  recently,  the  ultimate  or  small- 
est conceivable  division  of  matter  was  assumed  to  be  the 
atom  (Dalton,  1808).  Later  researches  of  radio-active  sub- 
stances have  developed  the  infinitely  smaller  particles  which 
have  been  termed  "electrons"  (Stoney,  1891)  and  "corpus- 
cles" (Thomson,  1897).  The  electron  is  assumed  to  be  a 
minute  particle  of  matter  having  a  negative  charge  of  elec- 
tricity; and  its  mass  is  variously  estimated  at  from  H?oo  to 
/^ooo  °f  the  mass  of  the  atom  of  hydrogen. 

The  chemical  divisions  of  matter  are  the  familiar  atoms 
and  molecules. 

Properties  of  Matter. — The  universal  attribute  of  all  matter 
is  that  described  as  "mass,"  which  may  be  simply  defined  as 
amount  of  matter.  By  virtue  of  its  assumed  electrical  state 
or  condition,  all  matter  is  endowed  with  certain  tangible  and 
measurable  qualities  or  properties,  such  as  weight,  inertia, 
density,  elasticity,  cohesion,  divisibility,  impenetrability,  ex- 
pansion, contraction. 

Matter  undergoes  many  changes  but  is  absolutely  inde- 
structible. 

Law  of  Attraction. — The  universal  law  of  attraction  is  that 
every  particle  of  matter  attracts  every  other  particle  of  mat- 


AIR  23 

ter,  the  force  of  attraction  varying  inversely  as  the  square  of 
the  distance  between  the  particles. 

Terrestrial  attraction  is  the  attraction  that  the  mass  of 
the  earth  exerts  on  the  mass  of  a  body.  This  is  commonly 
called  "gravitation"  and  the  attractive  force,  the  "force  of 
gravity"  or  simply  "gravity." 

Form  or  State  of  Matter. — All  matter  exists  in  one  of  three 
different  forms,  namely,  solid,  liquid,  or  gaseous.  The  same 
matter  may  pass  from  one  form  or  state  to  another  owing  to 
a  change  in  density. 

Molecular  State. — The  molecular  theory  assumes  that  all 
matter,  solid,  liquid  or  gaseous,  in  respect  to  its  physical  con- 
dition, is  composed  of  molecules,  each  complete  in  itself.  It 
is  assumed  that  these  molecules  are  subject  to  two  opposite 
or  opposing  forces  known  as  the  "molecular  forces"  of  at- 
traction and  repulsion. 

Molecular  attraction,  acting  to  bind  the  molecules  of  mat- 
ter together,  is  in  obedience  to  the  common  law  of  attraction 
in  all  matter. 

Molecular  Repulsion,  acting  to  drive  the  molecules  of  mat- 
ter apart,  is  the  result  of  a  state  of  incessant  molecular  vibra- 
tion, which  produces  the  effect  called  "heat." 

Solids. — Matter  in  the  solid  state  is  characterized  by  a 
greater  or  less  rigidity  of  its  molecules.  The  force  of  molecu- 
lar attraction  is  here  stronger  than  that  of  repulsion,  and  the 
molecules  are  held  in  a  firmer  grasp. 

Liquids. — -In  the  liquid  state,  the  forces  of  attraction  and 
repulsion  are  about  evenly  balanced,  and  the  molecules  move 
freely  among  each  other. 

Gases. — In  the  gaseous  state,  the  repulsive  forces  are  in  the 
ascendency  and  the  molecules  are  driven  so  far  apart  that  the 
density  of  the  matter  is  reduced  to  that  of  a  gas. 

Liquids  and  gases  are  both  fluids,  which  is  a  general  term 
applied  to  any  form  of  matter  other  than  a  solid. 

Illustration. — Ice,  water  and  steam  furnish  a  good  illustra- 
tion of  how  the  same  matter  can  pass  successively  from  the 
solid  to  the  liquid  and  gaseous  states.  In  the  passage 
from  one  state  to  another,  there  is  no  change  in  the  matter 


24  MINE  GASES  AND  VENTILATION 

itself,  the  difference  being  due  to  the  heat  condition  of  the 
mass. 

In  the  passage  from  solid  to  liquid,  or  from  liquid  to  gas 
or  vapor,  heat  is  given  out;  and,  vice  versa,  heat  is  absorbed 
when  a  gas  or  vapor  becomes  a  liquid,  or  a  liquid  becomes  a 
solid.  The  change  is  thus  a  heat  condition  only. 

Vapors  and  Gases.— The  term  vapor  properly  describes  the 
gaseous  condition  of  most  substances  that,  at  ordinary  tem- 
peratures, exist  as  liquid  or  solid ;  or  a  gas  at  or  near  its  point 
of  liquefaction.  The  term  thus  has  a  suggestive  meaning  of 
the  possible  liquid  or  solid  state  of  the  substance  now  in  the 
gaseous  state. 

The  term  gas,  on  the  other  hand,  is  a  general  term  that  re- 
lates solely  to  the  gaseous  condition  of  matter;  and  is  thus 
more  properly  applied  to  those  substances  that,  at  ordinary 
temperatures,  exist  as  gas;  although  they  may  be  liquefied  or 
solidified  by  a  decrease  of  temperature  and  an  increase  of 
pressure. 

Thus,  we  speak  of  air,  oxygen,  hydrogen,  nitrogen,  carbon 
dioxide,  methane,  etc.,  as  " gases,"  in  contrast  to  steam  (water 
vapor)  and  the  vapors  of  such  volatile  liquids  and  solids  as 
naphtha,  benzine,  camphor  and  other  similar  substances. 

Vaporization  takes  place  at  all  temperatures;  and  in  many 
instances,  a  substance  will  pass  directly  from  the  solid  to  the 
gaseous  condition,  without  becoming  liquid. 

Mass,  Volume,  Density. — Since  mass  is  amount  of  matter, 
the  mass  (M)  of  a  body  is  the  quantity  of  matter  it  contains, 
which  is  determined  by  the  volume  (V)  of  the  body  and 
the  density  (D)  of  the  matter.  The  relation  of  these  ele- 
ments is  expressed  by  the  formula 

M  =  VD 

Then,  considering  a  unit  volume  (V  =  1),  it  is  evident  that 
the  "unit  of  mass"  is  equal  to  the  "unit  of  density."  In  other 
words,  whatever  is  taken  as  the  accepted  unit  or  standard  of 
density  is  also  the  unit  and  standard  for  the  measurement  of 
mass,  which  is  the  ultimate  unit. 


AIR  25 

MEASUREMENT 

The  valuation  and  comparison  of  the  various  forms  and  condi- 
tions of  matter  and  the  estimation  of  physical  phenomena  are 
made  by  reference  to  three  general  standards  of  measurement, 
namely,  distance,  force  and  time.  There  are  many  modifica- 
tions and  combinations  of  these  three  elemental  standards. 

Distance. — This  includes  the  measurement  of  length,  sur- 
face and  volume,  all  of  which  are  derived  from  the  same 
standard  of  measure. 

Force. — -All  measurement  of  force  is  based  on  the  attractive 
force  exerted  by  the  earth  on  an  assumed  unit  of  mass  at  the 
surface  (sea  level),  in  any  given  latitude.  Mass  thus  becomes 
the  true  unit  in  this  measurement;  but  being  intangible,  the 
adopted  unit  is  the  pound,  which  represents  a  certain  definite 
mass,  taken  as  the  "unit  of  mass,"  for  purposes  of  measure- 
ment. A  force  is  measured  by  the  effect  of  its  action  on  a 
known  mass.  There  are  two  conditions:  1.  Static  condition 
(mass  fixed,  immovable),  force  applied  to  a  body  produces 
pressure,  weight.  2.  Dynamic  condition  (mass  free  to  move) 
force  produces  motion,  velocity. 

Under  these  two  conditions,  there  are,  therefore,  two  units 
of  force.  The  unit  of  measure  for  static  force  is  the  pound, 
while  the  unit  of  measure  for  dynamic  forces  is  the  force 
that  will  produce  a  unit  of  velocity  in  a  unit  of  mass,  in  a 
unit  of  time.  In  other  words,  the  force  that  will  increase  the 
rate  of  motion  of  a  unit  mass,  by  a  unit  distance,  in  a  unit  time. 

Application. — Applying  these  units  of  measure,  the  weight 
(W)  of  a  body,  expressed  in  pounds,  is  the  static  force  (F) 
acting  on  the  body,  due  to  gravity. 

Hence,  in  statics, 

F  =  W  (1) 

In  dynamics,  the  force  (Fi)  producing  motion  is  measured 
by  the  mass  (M)  of  the  body  and  the  velocity  (v)  produced 
per  unit  of  time.  Hence,  in  dynamics, 

Fi  =  Mv  .  (2) 

The  velocity  produced  may  be  constant  or  accelerated. 
Constant  velocity  is  the  distance  passed  over  in  a  unit  of 


26  MINE  CASES  AND  VENTILATION 

time.  Acceleration  is  the  gain  in  velocity  per  unit  of  time. 
A  constant  force,  as  gravity,  acting  on  a  body  free  to  move 
produces  a  uniform  acceleration;  that  is  to  say  the  gain  in 
velocity,  each  unit  of  time,  is  constant. 

Assuming  a  falling  body,  the  force  producing  motion  is 
the  weight  (W)  of  the  body,  and  the  gain  in  velocity  per 
unit  of  time  (acceleration  due  to  gravity,  g)  is  the  velocity 
produced  in  the  mass  (M).  Hence,  in  falling  bodies, 

W  =  Mg  (3) 

and 

M  =  Wg  (4) 

which  enables  the  calculation  of  the  mass  of  a  body  from  its 
weight. 

Combining  formulas  (2)  and  (3), 

Fi       v 
W   =  g 

Hence  a  force  acting  to  produce  motion  in  a  body  bears  the 
same  ratio  to  the  weight  of  the  body,  as  the  acceleration  due 
to  the  force  bears  to  the  acceleration  due  to  gravity.  Or,  ex- 
pressed as  a  proportion, 

FnWi-.v.g  (6) 

Time. — The  element  of  time  is  important  in  the  estimation 

of  velocity  and  power.     For  example,  to  traverse  the  same 

distance  in  one-half  the  time  will  require  twice  the  velocity. 

Likewise,  to  perform  the  same  work  in  one-half  the  time  will 

require  twice  the  power. 

Special  Units. — There  are  numerous  other  units  of  limited 

significance;  such  as  units  of  capacity,  pints,  quarts,  gallons, 

barrels,  etc.;  units  of  currency,   cents,  dimes,  dollars,  etc.; 

circular  units,  degrees,  radians,  etc.;  electrical  units,  amperes, 

volts,  ohms,  watts,  etc. 

Compound  Units. — Many  units  of  measure  are  composed  of 

two  or  more  simple  units.     The  following  are  examples: 

Unit  velocity — (distance)  -f-  (time)  Ft.  per  sec.,  or  ft.  per  min. 

Unit   work— (distance)     X     (force) Ft.-lb. 

Unit  power — (distance)  X  (force)  -f-  (time). .  .Ft.-lb.  per  min. 


AIR  27 

The  above  are  only  given  as  samples  of  many  similar  com- 
pound units;  such  as  inch-pounds;  miles  per  hour;  gallons  per 
hour;  cubic  feet  per  minute;  pounds  per  cubic  foot;  tons  per 
acre;  foot-acres,  etc. 

All  of  these,  it  will  appear,  are  derived  from  the  simple  units 
of  distance,  force,  time,  or  the  special  units  to  which  reference 
has  been  made. 

Energy. — Energy,  in  physics,  is  capacity  to  perform  work. 
It  is  the  vitalizing  force  that  is  manifested  in  matter  by  the 
familiar  agencies  of  heat,  light,  electricity,  magnetism,  molecu- 
lar attraction,  chemical  affinity,  etc.,  all  of  which  are  equally 
convertible,  one  into  the  other,  without  loss. 

The  physical  agencies  or  forms  of  energy  just  mentioned 
are  each  and  all  convertible  into  mechanical  motion,  which, 
again,  can  be  reconverted  into  heat,  light,  electricity,  and  mag- 
netism. This  fact  gives  rise  to  what  is  called  the  "mechanical 
equivalent"  in  reference  to  heat. 

Forms  of  Energy. — Energy  is  of  two  kinds  that  differ  from 
each  other  only  in  the  sense  that  one  (kinetic)  is  actual  and 
present,  while  the  other  (potential)  is  possible  only. 

Kinetic  energy  (E)  is  the  energy  possessed  by  a  body  by 
virtue  of  its  motion.  The  force  producing  an  acceleration  (/) 
in  a  mass  (Af),  or  the  " living  force"  in  the  body  (momentum), 
is  Mf.  The  acceleration  (/)  being  uniform  or  the  velocity  in- 
creasing uniformly,  the  distance  increase,  per  unit  of  time  is 
//2,  and  the  work  performed  in  producing  this  acceleration  is 
stored  in  the  body  as  "  kinetic  energy,"  by  virtue  of  which  the 
body  would  continue  to  move  at  the  velocity  imparted,  till 
opposed  by  some  force.  The  energy  stored  per  second  is  cal- 
culated by  the  formula 

Kinetic  energy,         E  =  Mf  X  |  =  J^M/2 

Potential  energy  is  the  energy  that  is  possessed  by  a  body 
by  virtue  of  the  position  or  state  in  which  it  is  held  or  re- 
strained so  that  motion  cannot  take  place  till  the  restraining 
force  is  removed.  Examples  of  bodies  having  potential  energy 
are,  a  suspended  ball,  a  confined  spring,  etc. 


28 


MINE  CASES  AND  VENTILATION 


A  common  method  of  making  physical  measurements  for 
the  estimation  of  weight,  volume,  heat,  etc.,  is  by  reference 
to  some  adopted  standard.  All  such  measurements  are  rela- 
tive and  are  frequently  termed  " specific."  Such,  for  example, 
are  specific  gravity,  specific  volume,  specific  heat,  etc.  The 
atomic  weight  of  elements  is  often  called  specific  weight. 

The  Elements. — An  element  is  a  substance  that  has  not,  as 
yet,  been  resolved  into  parts  of  a  different  nature  and  is, 
therefore,  regarded  as  being  composed  wholly  of  one  kind 
of  matter  or  simple,  in  contrast  with  a  compound,  which 
is  composed  of  two  or  more  elements  or  kinds  of  matter. 

The  following  table  gives  the  more  important  elements, 
together  with  their  chemical  symbols  and  specific  or  atomic 
weights : 

TABLE  OF  THE  MORE  IMPORTANT  ELEMENTS 
International  Committee  (1910) 


Elements 

Sym- 
bols 

Atomic 
weights 

Elements 

Sym- 
bols 

Atomic 
weights 

H  =  l 

0  =  16 

H  =  l     O  =  16 

Aluminum  
Antimony  

Al 
Sb 
A 
As 
Ba 
Bi 
B 
Br 
Cd 
Cs 
Ca 
C 
Ce 
Cl 
Cr 
Co 
Cb 
Cu 
F 
Au 
He 
H 
I 
Ir 
Fe 
Pb 
Li 
Mg 

26.9 
119.3 
39.6 
'74.36 
136.27 
206.34 
10  91 
79.28 
111.5 
131  .75 
39.77 
11.9 
139.13 
35.18 
51  .58 
58.5 
92.75 
63.06 
18.85 
195.62 
3.97 
10 
125.9 
191.56 
55.4 
205.44 
6.94 
24.13 

27.1 
120.2 
39  9 
74.96 
137.37 
208  0 
11  .0 
79.92 
112.4 
132.81 
40.09 
12  0 
140.25 
35.46 
52.0 
58.97 
93.5 
63.57 
19.0 
197.2 
4.0 
1.008 
126.92 
193.1 
55.85 
207.1 
7.0 
24.32 

Manganese  
Mercury  
Molybdenum 

Mn 
Hg 
Mo 
Ni 
N 
Os 
0 
Pd 
P 
Pt 
K 
Ra 
Rh 
Se 
Si 
Ag 
Na 
Sr 
S 
Te 
Tl 
Sn 
:  Ti 
W 

u 
v 

Zn 

Zr 

54.49 
198.4 
95  23 
58.21 
13  9 
189.37 
15.88 
105.9 
30.77 
193.44 
38.78 
224.6 
102.08 
78.6 
28.1 
107.02 
22.82 
86.92 
31.81 
126.48 
202   37 
118.05 
47  72 
182.53 
236.59 
50.79 
64.85 
89.88 

54.93 
2CO  0 
96.0 
58.68 
14.01 
190.9 
16   0 
106.7 
31.0 
195.0 
39.1 
226.4 
102.9 
79.2 
28.3 
107.88 
23.0 
87.62 
32  07 
127.5 
204.0 
119.0 
48.1 
184.0 
238.5 
51.2 
65.37 
90.6 

Arsenic  
Barium  
Bismuth  
Boron 

Nickel  
Nitrogen  
Osmium  
Oxygen  
Palladium  
Phosphorus  

Bromine 

Cadmium  

Calcium  
Carbon  
Cerium  

Potassium 

Radium  
Rhodium  
Selenium  
Silicon  
Silver  

Chlorine  

Chromium 

Cobalt 

Columbium  
Copper  
Fluorine  
Gold  

Sodium  
Strontium  
Sulphur  
Tellurium  
Thallium  . 
Tin  
Titanium  

Helium 

Hydrogen  
Iodine.  . 

Iridium.  .  .  . 

Tungsten  
Uranium  
Vanadium  
Zinc  
1  Zirconium  6 

ylron  

Lead  

Lithium  
Magnesium  

AIR  29 

The  preceding  table  contains  only  56  out  of  the  80  or  more 
elements  that  have  been  discovered,  many  of  which  are  so 
rare  as  to  be  of  little  practical  importance.  The  values  of 
the  atomic  weights  are  given  referred  both  to  hydrogen  as 
unity  and  oxygen  as  16.  The  heavy  type  indicates  the  values 
commonly  used  in  the  study  of  mine  gases. 

DENSITY  AND  VOLUME 

Density  Defined. — The  term  "  density  "  refers  to  the  amount 
of  matter  in  a  given  volume  or  space.  The  commonly  adopted 
measure  of  density  is  the  ratio  of  the  weight  of  a  body  to  its 
volume  or  the  space  it  occupies,  as  expressed  by  the  formula : 

~       ._,          weight 
Density  =  — r-- 
volume 

In  a  general  sense,  the  term  density  has  thus  come  to 
mean  the  weight  per  unit  volume.  For  example,  the  density 
of  water  is  commonly  understood  to  mean  its  weight  per 
cubic  foot  (62.4283  lb.,  max.  dens.,  4°C.). 

Specific  or  Atomic  Volume. — These  terms  have  reference  to 
an  assumed  unit  volume  for  all  gases,  which  unit  is  the  as- 
sumed vo'.ume  of  a  single  gaseous  atom. 

Avogadro's  Law  of  Gaseous  Volume. — This  law  may  be 
stated  briefly  and  clearly  as  follows : 

At  the  same  temperature  and  pressure  all  gaseous  molecules 
are  assumed  to  be  of  the  same  size. 

With  a  few  unimportant  exceptions,  this  law  applies  to  all 
gases,  whether  simple  or  compound.  It  holds  true  for  all  mine 
gases  and  is  important  in  the  calculation  of  the  relative  volume 
of  gases  concerned  in  chemical  reactions. 

Molecular  Volume. — Chemical  hypothesis  assumes  that  the 
molecules  of  simple  substances  each  contain  two  atoms  only, 
while  the  molecules  of  a  compound  substance  may  contain  any 
number  of  atoms,  but  never  less  than  two.  Notwithstanding 
this  multiplicity  of  atoms,  Avogadro's  law  makes  all  gases, 
with  a  few  unimportant  exceptions,  to  contain  the  same  num- 
ber of  molecules,  per  unit  volume,  when  measured  at  the  same 
temperature  and  pressure.  In  other  words,  measured  at  the 


30  MINE  GASES  AND  VENTILATION 

same  temperature  and  pressure,  all  gaseous  molecules  are  of 
the  same  size. 

Calculation  of  Density. — The  elements  form  the  basis  of  all 
relative  measurements  with  respect  to  volume,  density  and 
weight.  For  example,  the  density  of  air,  referred  to  hydrogen 
as  unity  (H  =  1),  can  be  calculated  from  the  relative  weights 
and  volumes  of  oxygen  and  nitrogen,  which  are  the  chief 
constituents  of  air.  The  composition  of  pure  air,  by  volume, 
is  practically,  oxygen  (O),  20.9  per  cent.;  nitrogen  (N),  79.1 
per  cent.  Then,  since  the  atomic  weight  of  oxygen  is  16  and 
that  of  nitrogen  14,  the  relative  weight  of  100  volumes  of  air, 
referred  to  hydrogen  as  unity,  is  found  as  follows: 

Oxygen,  20.9  X  16  =    334.4 

Nitrogen,  79.1  X  14  =  1107.4 


Air,  100  vol's   =  1441.8 

Therefore,  one  volume  of  air  is  1441.8  -r-  100  =  14.418  times 
as  heavy  as  the  same  volume  of  hydrogen;  or,  the  density  of 
air  referred  to  hydrogen  is  14.418. 

The  percentage  composition  of  pure  air,  by  weight,  is 
readily  calculated  from  the  above  figures;  thus: 

Oxygen,       (334.4  X  100)  -r-  1441.8  =  say  23.2  per  cent. 
Nitrogen,  (1107.4  X  100)  -r-  1441.8  =  say  76.8  per  cent. 

SPECIFIC  GRAVITY 

The  specific  gravity  of  a  substance — solid,  liquid,  or  gas — 
is  the  ratio  of  the  weight  of  that  substance  to  the  weight 
of  another  substance  taken  as  a  standard,  volume  for  volume; 
„  wt.  of  unit  vol.  of  substance 

W/vj        /IT*          — T      — -  -  -, • 

wt.  of  unit  vol.  of  standard 

Comparison  of  Standards. — Hydrogen,  air  and  water  are 
the  three  standards  commonly  used  in  the  determination  of 
the  specific  gravity  of  gases,  liquids  and  solids.  The  relative 
densities  of  these  standards  are  as  follows : 

Air  (dry)  is  14.418  times  as  heavy  as  hydrogen,  at  the  same 
temperature  and  pressure,  volume  for  volume. 


AIR  31 

Water  (max.  density,  4°C.)  is  773  times  as  heavy  as  dry 
air  at  32  deg.  F.,  bar.  29.92  in.;  and  815  times  as  heavy  as  dry 
air  at  60  deg.  F.,  bar.  30  in.,  volume  for  volume. 

Standard  for  Gases. — The  standard  adopted  for  gases  is  air 
or  hydrogen,  of  the  same  temperature  and  pressure  as  the  gas. 

Standard  for  Liquids  and  Solids. — The  standard  adopted  for 
liquids  and  solids  is  water  at  maximum  density.  Except 
where  great  accuracy  is  desired,  the  weight  of  1  cu.  ft.  of 
water  is  taken  as  62.5  Ib.  Exactly,  1  cu.  ft.  of  pure  water,  at 
maximum  density  weighs  62.4283  Ib.;  or  1  cu.  in.  weighs 
252.89  grains  =  0.03613  Ib. 

Calculation  of  the  Specific  Gravity  of  Gases. — Since  air  is 
14.4  times  as  heavy  as  hydrogen,  at  the  same  temperature 
and  pressure,  the  specific  gravity  of  a  gas,  referred  to  air  as 
unity,  can  be  calculated  by  dividing  one-half  of  its  molecular 
weight  by  14.4.  For  example,  the  molecular  weight  of  carbon 
dioxide  is  44;  therefore,  44  -f-  2  =  22,  and  22  -r-  14.4  =  1.528. 
The  actual  specific  gravity  is  1.529. 

Finding  Specific  Gravity  of  Gases. — A  glass  globe,  any  con- 
venient size,  is  first  weighed  empty  (air  exhausted),  w;  then 
full  of  air,  w\\  and,  lastly,  filled  with  the  gas,  w*:  the  tem- 
perature and  pressure  remaining  constant. 

wz  —  w 
Sp.  gr.  = 


Finding  Specific  Gravity  of  Liquids. — A  glass-stoppered  bot- 
tle is  first  weighed  empty,  w;  then  filled  with  water  w\\  and, 
lastly,  filled  with  the  liquid,  w%.  The  specific  gravity  is  then 
calculated  by  the  above  formula  for  gases.  Or,  the  specific 
gravity  is  determined  by  a  graduated  float  (hydrometer). 

Finding  Specific  Gravity  of  Solids. — Weight  of  the  solid  in 
air,  wmj  weight  immersed  in  water  w\.  The  weight  of  the 
water  displaced  is  then  w  —  10 1,  which  has  the  same  volume 
as  that  of  the  solid. 

Sp.  gr. 


32  MINE  GASES  AND  VENTILATION 

SPECIFIC   GRAVITIES   AND   UNIT  WEIGHTS   OF  SOLIDS   AND   LIQUIDS 


Substance 

Average 
specific  gravity 
(water  =  1) 

Average 
weight  (Ib. 
per  cu.  ft.) 

Alcohol  pure 

0  793 

49  5 

commercial  
Aluminum          

0.834 
2  66 

52.1 
166  0 

Asphalt  (1  to  1.8) 

1  4 

87  0 

Brass,  east  (7.8  to  8.4)  

8.1 

506  0 

rolled  

8  4 

525  0 

Brick,  pressed 

2  4 

150  0 

common,  hard  

2.0 

125  0 

Brickwork,  masonry  (1.8  to  2.3)  
Bronze  (8.7  to  8.9)  
Clay  (1.8  to  2.6)  

8.8 
2.2 

110  to  140 
550.0 
137  5 

Coal,  anthracite  (1.3  to  1.7)  
bituminous  (1.2  to  1.5)  
cannel,  gas  coal  (1.18  to  1.28)  .  .  .  . 
lignite,  brown  coal  
Coke,  loose  piled 

1.5 

1.3 
1.23 
1.1 

93.75 
81.25 
76.88 
68.75 
20  to  25  0 

Concrete  

2.3 

144.0 

Copper,  cast  (8.6  to  8.8)  
rolled  (8.8  to  9) 

8.7 
8  9 

543.0 
556  0 

Earth,  dry,  loose  to  well  rammed  
moist,  loose  to  well  rammed.  .  .  . 
wet,  flowing  mud 

76  to  95  .  0 
78  to  96.0 
105  to  115 

Granite  (2  56  to  2  88) 

2  72 

170  0 

Gold,  cast  (18.29  to  19.37)   

18  83 

1176  0 

Gravel,  loose 

95  to  100 

Gypsum,  ground  or  calcined,  loose  
well  shaken  
Ice 

0  92 

56.0 
64.0 
57  5 

Iron,  cast  (6.9  to  7.4)  
rolled  
wrought,  sheet  (7.6  to  7.9)  
Lead  (11.3  to  11.47)  
Lime  (quicklime)  
ground,  loose  (66  Ib.  per  bus.)  .... 
Limestone  

7.2 
7.68 
7.8 
11.38 
1.5 

2.7 

450.0 
480.0 
485.0 
710.0 
93.75 
53.0 
168.0 

Marble  (2.5  to  2.8)  
Mercury  (32  deg.  F.)  
(62deg.  F.).. 

2.65 
13  .  593 
13.555 

165.0 
850.0 
847.0 

AIR  33 

Pitch 1.155  72.0 

Platinum 21.6  1348.0 

Rosin 1.1  68.67 

Sand,  dry 100.0 

wet. 130.0 

Sandstone  (2.1  to  2.7) 2.4  150 . 0 

Shale  (2.4  to  2.8) 2.6  162.0 

Silver 10.5  655.0 

Slate  (2.7  to  2.9) 2.8  175.0 

Steel  (7.8  to  7.9) 7.85  490.0 

Sulphur 2.0  125.0 

Tallow 0.94  58.7 

Tar 1.0  62 . 5 

Tin,  cast  (7.2  to  7.5) 7.35  459,0 

Traprock 3.0  187.0 

Water  (max.  density,  4°C.) 1.0  62.428 

(pure,  62°F.) 0.999  62.366 

(pure,  212°F.) 0 . 958  59 . 806 

sea,  average 1  •  028  64 . 176 

WEIGHT  OF  WOODS   (DKY,  SEASONED) 

Lb.  per  cu.  ft. 

Ash,  white 38 

Birch 41 

Cedar,  white 23 

red 35 

Cherry 42 

Chestnut 41 

Elm 35 

Ebony 76 

Hemlock 25 

Hickory 53 

Mahogany,  Spanish 53 

Honduras 35 

Maple 49 

Oak,  live 59 

white 48 

black,  jack,  etc 35  to  45 

Pine,  white. 25 

yellow,  Northern 34 

Southern 45 

Poplar  (cottonwood) 33 

Spruce 25 

Sycamore 37 

Walnut 37 

3 


34  MINE  GASES  AND  VENTILATION 

SPECIFIC   GRAVITIES   AND  WEIGHTS  OF  OILS 


Sp.  Gr. 

Lb.  per  Gal. 

Animal  —  lard  

0.916 

7.64 

sperm  (pure)  

.  0  .  880 

7.34 

whale  

0.925 

7.72 

Vegetable  —  cottonseed  

....     0.923 

7.70 

linseed  (raw)  

0  .  933 

7.79 

(boiled)  

0.780 

6.51 

olive  

0.917 

7.65 

rape  (colza)  

0.915 

7.63 

Mineral  —  petroleum  (crude)  

0  .  77-1  .  06 

gasoline  

..     0.700 

5.84 

kerosene  (coal  oil)  

...     0.800 

6.68 

naphtha  

0.730 

6,09 

Use  of  Specific  Gravity. — To  find  the  weight  of  any  volume 
of  a  substance,  multiply  the  unit  weight  of  the  standard,  by 
the  specific  gravity  of  the  substance,  and  that  product  by  the 
given  volume;  or,  expressed  as  a  formula, 

Wt.  =  unit  weight  of  standard  X  sp.  gr.  X  vol. 

For  example,  taking  the  average  specific  gravity  of  anthra- 
cite coal  as  1.5  the  weight  of  this  coal  underlying  1  acre 
(43,560  sq.  ft.)  of  land,  for  a  thickness  in  the  seam  of  1  ft.; 
or,  as  we  say,  per  foot-acre,  in  long  tons  (2240  Ib.)  is 

62.5  X  1.5  X  43,560 

00,n  =  1823  long  tons 

ZZ^±(J 

Or,  taking  the  weight  of  1  cu.  ft.  of  air  (60°F.,  bar.  30  in.) 
as  0.0766  Ib.,  since  the  specific  gravity  of  carb.on  dioxide  (CO2) 
referred  to  air  as  unity  is  1.529,  the  weight  of  100  cu.  ft.  of 
this  gas,  at  the  same  temperature  and  pressure,  is 

0.0766  X  1.529  X  100  -  11.712+  Ib. 

OCCLUSION,  EMISSION,  DIFFUSION  OF  GASES 

Occlusion  of  Gases. — The  occlusion  of  gases  in  coal  or  other 
solid  substances  is  the  result  of  the  absorptive  power  of  the 
substance  for  that  particular  gas.  For  example,  platinum, 
palladium,  gold  and  other  metals,  as  well  as  coal  (carbon), 
absorb  varying  quantities  of  hydrogen,  nitrogen,  oxygen, 
the  hydrocarbon  and  other  gases. 


AIR  35 

The  most  common  examples  of  occlusion  are  the  absorp- 
tion of  hydrogen  by  platinum;  and  of  methane,  nitrogen,  oxy- 
gen and  carbon  dioxide  by  coal  and  coal  dust.  The  law  that 
governs  this  absorption  is  unknown.  The  occluded  gas  is 
often  held  very  strongly  by  the  substance  with  which,  how- 
ever, it  is  not  combined. 

The  occluded  gases  of  coal  seams  were  probably  produced 
in  the  metamorphic  processes  that  formed  the  coal;  and  their 
absorption  (occulsion)  in  the  solid  formation  may  have  re- 
sulted in  the  oxidation,  to  a  limited  extent,  of  the  carbon- 
aceous matter  that  was  being  transformed  into  coal.  Such 
reactions,  if  taking  place  in  the  measures,  together  with  the 
consolidation  that  accompanied  the  formation,  would  natur- 
ally give  rise  to  the  observed  pressures  of  occluded  gases. 

The  pressure  of  occluded  gases  in  coal  formations  is  very 
variable,  depending  not  only  on  the  conditions  attending  the 
occlusion;  but  to  an  even  greater  extent  on  the  impermea- 
bility of  the  infolding  strata,  which  has  prevented  the  escape 
of  the  gases  from  the  measures  where  they  are  formed. 

Transpiration,  Emission  of  Gases  from  Coal. — The  gases 
occluded  in  coal  exude  from  its  exposed  surface  in  the  same 
manner  as  perspiration  exudes  from  the  pores  of  the  skin. 
The  term  " transpiration"  relates  to  the  motion  of  a  gas 
through  a  capillary  tube  and  thus  describes  the  emission  of 
gas  from  coal. 

The  velocity  of  transpiration  is  according  to  a  different 
law  from  that  governing  the  rate  of  the  diffusion  of  gases. 
For  the  same  gas,  the  rate  of  transpiration  varies  directly 
as  its  pressure  or  density,  and  inversely  as  the  length  of  the 
tubes  through  which  it  must  pass.  The  velocity  of  trans- 
piration is  independent  of  the  material  that  forms  the  tube, 
but  is  affected  by  temperature,  being  less  for  a  higher  tem- 
perature, and  vice  versa. 

RELATIVE  VELOCITY  OF  GASES  (AIR  =  1) 
Gas  Rel.  Veloc.  Gas  Rel.  Veloc. 

Hydrogen 2 . 066     Carbon  dioxide 1 . 237 

Olefiant  gas 1 . 788     Carbon  monoxide 1 . 034 

Methane '. 1 .639     Nitrogen 1 . 030 

Hydrogen  sulphide 1 .458     Oxygen 0.903 


36  MINE  GASES  AND  VENTILATION 

The  above  table  gives  the  relative  rates  or  velocities  with 
which  the  common  mine  gases  transpire,  referred  to  the  rate 
for  air  as  unity.  The  actual  rate  of  emission  of  gas  from 
coal,  however,  will  depend  chiefly  on  the  pressure  of  the  gas 
in  the  coal  Any  sudden  fall  in  barometric  pressure  is  always 
accompanied  with  an  increase  in  the  emission  of  gas  from 
the  coal,  but  the  increase  is  almost  inappreciable. 

Diffusion  of  Air  and  Gases. — If  the  molecules  of  all  matter 
are  assumed  to  be  in  a  constant  state  of  vibration,  it  nat- 
urally follows  that  the  vibratory  movement  or  force  will  vary 
with  the  density  of  the  matter.  In  the  case  of  fluids — air, 
gas,  or  liquid — 'the  molecules  are  free  to  move  among  them- 
selves, which  is  not  true  of  solids,  whose  molecules,  normally, 
hold  fixed  relations  to  each  other. 

If  the  densities  of  two  fluids  are  equal,  the  vibratory  force 
is  equal  in  each  fluid;  and,  at  the  plane  of  contact  of  the  two 
fluid  bodies,  action  and  reaction  are  equal  between  the  vi- 
brating molecules  and  there  is  no  tendency  of  these  fluids  to 
mix.  The  laws  governing  the  mixture  of  liquids  is  not  as 
simple  as  in  the  case  of  gases,  owing  chiefly  to  numerous 
physical  properties  of  liquids  that  modify  and  retard  the 
diffusive  action.  While  the  diffusion  of  gases  into  each  other 
and  into  air  is  extremely  rapid,  the  diffusion  of  liquids  is 
often  very  slow  and  in  some  cases  does  not  take  place  at  all 
because  of  the  counteracting  forces. 

Gases  of  different  densities  diffuse  into  each  other  and 
into  air.  The  action  is  extremely  rapid  and  conforms  very 
closely  to  certain  well  defined  laws.  The  diffusion  of  mine 
gases  into  the  mine  air  and  into  the  air  current  is  an  impor- 
tant feature  of  mine  ventilation. 

Law  of  Diffusion  of  Air  and  Gases. — By  a  similar  experi- 
ment, showing  the  diffusion  of  hydrogen  into  oxygen,  Graham 
found  that  for  every  volume  of  oxygen  that  passed  into  the 
hydrogen,  four  volumes  of  the  hydrogen  passed  into  the  oxy- 
gen, the  ratio  thus  being  4:1,  in  this  case.  But,  calling  the 
density  of  hydrogen  unity  or  1,  that  of  oxygen  is  16  and 
A/16  =  4.  This  and  other  similar  experiments,  all  confirming 
the  first;  led  Graham  to  propound  the  following  law: 


AIR  37 

Graham's  Law. — The  velocity  or  rate  of  diffusion  of  air 
and  gases  varies  inversely  as  the  square  roots  of  their  densi- 
ties or  specific  gravities,  density  being  referred  to  hydrogen 
as  unity,  and  specific  gravity  to  air. 

This  law  is  simply  expressed  by  the  following  formulas: 

Rel.  vel.  of  diffusion  (hydrogen  :  gas)  =  — -= 

V  density  of  gas 

Rel.  vel.  of  diffusion  (air :  gas)  =  — -j=. 

V  sp.  gr.  of  gas 

Experiment. — The  diffusion  of  air  and  gases  has  been  shown 
to  take  place  through  certain  substances  with  practically  the 
same  rapidity  as  when  they  are  in  direct  contact.  The  dif- 
fusion of  hydrogen  into  air  is  well  shown  by  the  following 
simple  experiment.  A  glass  tube,  say  18  or  20  in.  long,  1-in. 
bore,  is  closed  at  one  end  with  a  plug  of  plaster.  The  tube  is 
first  filled  with  the  gas  and  the  open  end  then  immersed  be- 
neath the  surface  of  a  basin  of  mercury.  At  once  the  mercury 
is  observed  to  rise  slowly  in  the  tube  to  take  the  place  of  the 
hydrogen  that  is  passing  out  through  the  plug  and  escaping 
into  the  air.  Investigation  shows,  however,  that  while  hydro- 
gen has  passed  out  of  the  tube,  some  air  has  passed  into  the 
tube,  as  there  remains  in  the  tube  a  mixture  of  hydrogen  and 
air. 

Illustration  of  Graham's  Law. — The  relative  velocities  or  rates  of 
diffusion  of  different  gases  (hydrogen  =  1)  are  calculated  from  their 
respective  densities  referred  to  hydrogen  as  unity ;  thus, 

Methane  (CH4);  density,  8;  Rel.  vel.  =  —L  =  -±—  =  0.354  (H  =  \] 

•y/g  Z.828 

In  like  manner,  the  relative  velocities  or  ratio  of  diffusion  of  different 
gases  (air  =  1)  are  calculated  from  their  respective  specific  gravities, 
referred  to  air  as  unity;  thus, 

Carbon  dioxide  (CO2);  sp.  gr.,  1.529;  v  =      ,  =  0.808 

*-529  (Air  =  l) 

Methane  (CH4);  sp.  gr.,  0.559;  v  =  -y==  =  1.337 

V  0.559 

Experiment  Showing  Effect  of  Diffusion. — An  interesting 
experiment,  showing  the  relative  increase  or  decrease  of  the 
volume  of  gas  contained  in  a  vessel  owing  to  diffusion,  is 


38 


MINE  GASES  AND  VENTILATION 


illustrated  in  Fig.  5.  The  velocity  of  diffusion  of  methane 
being  greater  than  that  of  carbon  dioxide,  when  the  latter 
is  contained  in  the  inner  jar  and  the  former  in  the  outer  bell- 
jar  the  bladder  is  expanded,  because  the  methane  passing 
into  the  small  jar  is  greater  in  volume  than  the  carbon  di- 
oxide passing  out.  Again,  the  bladder  is  depressed  when 
the  gases  change  places. 


FIG.  5. 

Composition  of  Gases. — Gas,  like  other  material  substances, 
is  composed  of  the  elements  of  matter.  A  simple  or  element- 
ary gas  is  composed  wholly  of  one  kind  of  matter;  as  hydro- 
gen (H),  oxygen  (O),  nitrogen  (N),  etc. 

Many  gases,  like  many  solids  and  liquids,  are  compound. 
The  molecule  of  such  a  gas  is  formed  by  the  chemical  union 
of  two  or  more  atoms  of  different  elements;  as  methane 
(CH4),  carbon  monoxide  (CO),  carbon  dioxide  (CO2),  etc. 

A  gaseous  mixture  is  a  mechanical  mixture  of  different 
gases,  simple  or  compound.  These  gases  are  mixed  together 
in  any  proportion,  but  are  not  chemically  united. 

Firedamp  is  a  mechanical  mixture  of  a  combustible  gas 
or  gases  with  air  in  such  proportions  as  to  render  the  mix- 
ture inflammable  or  explosive.  The  term,  however,  is  gener- 
ally understood  to  mean  an  inflammable  or  explosive  mixture 


AIR  39 

of  methane  (CH4)  and  air.  In  English  and  other  foreign  text- 
books, the  term  "firedamp"  is  improperly  applied  to  any  mix- 
ture of  explosive  gas  and  air,  without  regard  to  whether  the 
proportions  are  within  the  inflammable  or  explosive  limits  of 
the  gas.  Such  a  mixture  will  not  inflame  or  explode  and  is 
not,  properly  speaking,  a  firedamp  mixture. 

Percentage  Composition  by  Weight.  —  By  the  "percentage 
composition"  of  a  compound  is  generally  meant  the  percent- 
age, by  weight,  of  each  element  composing  the  substance. 
This  is  calculated  from  the  ratio  of  the  relative  weight  of 
each  constituent  element  to  its  molecular  weight.  The  term 
"  percentage  composition"  may  refer,  however,  to  the  per- 
centage by  volume  of  each  constituent  element. 

For  example,  a  molecule  of  methane  (CH4)  contains  one 
•atom  of  carbon  and  four  atoms  of  hydrogen.  Then,  since  the 
atomic  weight  of  carbon  is  12  and  that  of  hydrogen  1,  the 
molecular  weight  of  methane  is  12  -h  (4  X  1)  =  16,  and  the 
percentage  composition  of  this  gas  is  calculated  as  follows: 

Carbon(C);  atomic  weight,  12;  relative  weight  .....  12 
Hydrogen  (H4)  ;  atomic  weight,  1  ;  relative  weight,  4X1=  4 

Molecular  weight  of  gas   ...    .......    16 

The  percentage  of  each  constituent  element  is  then  : 
Carbon.  .................  i%6  (100)  =  75  per  cent. 

Hydrogen  .................  £{6  (100)  =  25  per  cent. 


100  per  cent. 

In  like  manner,  a  molecule  of  carbon  dioxide  (CO2)  con- 
tains one  atom  of  carbon  and  two  atoms  of  oxygen.  The 
atomic  weight  of  carbon  being  12  and  that  of  oxygen  16,  the 
molecular  weight  of  carbon  dioxide  is  12  +  (2  X  16)  =  44,  and 
the  percentage  composition  of  the  gas  is  found  as  follows: 

Carbon  (C);  atomic  weight,  12;  relative  weight  .....    12 
Oxygen  (O2);  atomic  weight,  16;  relative  weight,  2  X  16  =32 

Molecular  weight  of  gas   ...........  44 


40  MINE  GASES  AND  VENTILATION 

The  percentage  composition  is  then : 

Carbon i%4  (100)  =  27.27  per  cent. 

Oxygen s%4  (100)  =  72.73  per  cent. 


100.00  per  cent. 

Percentage  by  Volume. — When  applied  to  a  gaseous  mix- 
ture the  term  " percentage  composition"  is  usually  taken  as 
referring  to  the  percentage  by  volume  of  the  several  gases 
forming  the  mixture,  unless  otherwise  stated.  The  method  of 
making  this  calculation  is  given  on  page  102. 

Specific  Gravity  of  Mixtures  of  Gases. — When  different  vol- 
umes of  gases  of  different  densities  are  uniformly  mixed  the 
density  of  the  mixture  is  determined  by  dividing  the  combined 
weight  of  the  mixed  gases  by  the  total  volume  of  the  mixture, 
which  will  give  the  unit  weight  or  the  weight  per  unit  of 
volume  of  the  mixture. 

The  actual  weights  of  the  gases  may  not  be  known,  but 
only  the  volume  of  each  gas  and  its  density  or  specific  gravity. 
In  that  case,  multiply  the  density  of  each  gas  by  its  volume, 
add  the  products  together  and  divide  the  sum  by  the  total 
volume  of  the  mixture;  the  quotient  obtained  will  be  the 
required  density  of  the  mixture. 

Or,  in  like  manner,  multiply  the  specific  gravity  of  each 
gas  by  ts  volume,  and  divide  the  sum  of  these  products  by 
the  total  volume  of  the  mixture,  and  the  quotient  obtained 
will  be  the  specific  gravity  of  the  mixture. 

Calculation. — For  illustration,  let  it  be  required  to  calculate  the 
specific  gravity  of  flashdamp,  which  has  a  theoretical  composition  of 
1658  volumes  of  methane  (CH4)  to  each  1000  volumes  of  carbon  dioxide 
(CO-.).  The  process  is  as  follows: 

Volume       Sq.gr.^I6^1- 

Methane 1658  X  0.559  =    926.8 

Carbon  dioxide. .  .    1000  X  1.529  =  1529.0 


2658  2455.8 

The  specific  gravity  of  the  flashdamp  is  then  calculated,  in  accordance 
with  the  above  rule,  as  follows: 

relative  wt.  (air  =  1)       2455.8  7 

Sp.  gr.  = j—-. —   y-r — =—*  ~    0-go    =  0.924,  nearly 

v  -  relative  total  vol.  2658 


AIR  41 

Calculation  Based  on  the  Law  of  Diffusion  of  Gases. — If 

two  gases  diffuse  into  each  other,  directly,  without  being  di- 
luted with  air,  the  volumes  of  the  gases  are  inversely  propor- 
tional to  the  square  roots  of  their  densities  or  specific  gravities. 
This  law  makes  it  possible  to  calculate  the  density  or  specific 
gravity  of  such  an  undiluted  mixture  of  two  gases  directly 
from  their  densities  or  specific  gravities,  without  reference 
to  their  relative  volumes.  This  is  accomplished  by  means  of 
the  formula 

_  a  Vfr  +  b\/g 
Va  +  VT 

in  which  D  =  density  or  specific  gravity  of  the  mixture;  a  and 
6  =  the  corresponding  densities  or  specific  gravities  of  the 
two  gases,  respectively. 

Calculation. — For  illustration,  let  it  be  required  to  calculate  the 
specific  gravity  of  flashdamp  (undiluted  mixture  of  methane  and  carbon 
dioxide)  directly  from  the  specific  gravities  of  these  gases;  methane  =0.559 
and  carbon  dioxide  =  1.529.  The  process  is  as  follows: 

Q.559VL529  +  1.529\/a559 

Sp.gr.  = 7 —  — ; —   -  =  0.924 

A/0.559  +  Vl.529 


SECTION  II 
HEAT 

SOURCES    AND    MEASUREMENT    OF    HEAT — CHEMISTRY    OF 
GASES — THERMOCHEMISTRY — HYGROMETRY— STEAM 

Definition. — Heat  is  DOW  understood  to  be  a  form  of  motion. 
All  matter  is  assumed  to  be  in  a  state  of  molecular  vibra- 
tion. The  rapidity  of  the  vibration  depends  on  the  degree  of 
heating  of  the  mass.  The  theory  assumes  that  the  amplitude 
of  the  vibrations  or  the  swing  of  the  molecules  is  greater  as 
the  density  of  the  mass  is  less.  This  would  lead  naturally 
to  the  conclusion  that  pressure,  which  increases  the  density 
of  matter,  will  decrease  the  amplitude  and  increase  the  rapid- 
ity of  vibration. 

Heat  is  thus  assumed  to  be  a  form  of  energy,  the  ampli- 
tude and  rapidity  of  the  vibrations  being  functions,  respec- 
tively, of  pressure  and  velocity,  the  factors  of  energy,  in 
mechanics.  The  theory  is  well  supported  by  observed  facts, 
as  the  blow  of  a  hammer  or  the  friction  of  rubbing  surfaces 
alike  develop  heat. 

Heat  in  Bodies. — Assuming  that  heat  is  a  form  of  molecu- 
lar vibration,  which  varies  in  different  kinds  of  matter,  it 
is  clear  that  each  kind  of  matter  has  its  own  peculiar  ca- 
pacity for  heat.  This  is  shown  to  be  the  case  by  the  fact 
that  different  bodies  when  exposed  to  the  same  source  of 
heat  are  heated  differently.  For  example,  when  equal  weights 
of  water  and  mercury  are  exposed,  for  the  same  time,  to  the 
same  heat  it  is  found  that  the  mercury  becomes  much  hotter 
than  the  water.  When  water  and  mercury  at  the  same  tem- 
perature are  allowed  to  cool  in  the  atmosphere,  the  air  ab- 
sorbing the  same  heat  from  each,  the  mercury  is  found  to 
cool  much  quicker  than  the  water.  It  is  evident  that  the 
water  absorbs  more  heat  and  gives  out  more  heat,  per  pound, 

42 


HEAT 


43 


than  the  mercury,  for  the  same  change  in  temperature.     In 
other  words,  water  has  a  greater  heat  capacity. 

Temperature. — The  temperature  of  any  body  or  mass  of 
matter  is  the  degree  of  heat  it  can  radiate  or  impart  to  other 
bodies  or  matter  with  which  it  is  in  contact;  or,  in  other 
words,  the  degree  of  sensible  heat  of  the  body.  It  is  not  the 
amount  of  heat  in  the  body;  as  water  contains  20  times  the 
quantity  of  heat  contained  in  an 
equal  weight  of  mercury,  at  the 
same  temperature. 

The  temperature  of  a  body  de- 
pends on  the  quantity  of  heat  the 
body  contains,  per  unit  weight,  and 
its  heat  capacity.  A  body  or 
matter  having  a  large  heat  capacity 
will  have  a  comparatively  low 
temperature. 

How  Temperature  is  Measured. 
Temperature  is  measured  by  the 
thermometer,  an  instrument  so 
common  as  to  need  no  description. 
The  principle  involved  is  that  the 
expansion  of  the  liquid  contained 
in  the  bulb  of  the  thermometer 
is  much  magnified  in  the  capillary 
stem.  Any  rise  of  temperature  is 
thus  clearly  indicated  by  a  cor- 
responding rise  of  the  liquid  in  the 
stem  and  a  fall  of  temperature  is 
likewise  accompanied  by  the  con- 
traction of  the  liquid,  which  drops 
in  the  stein. 

Two  Scales. — There  are  two  principal  thermometer  scales, 
the  Fahrenheit  and  the  centigrade.  These  are  each  cali- 
brated with  reference  to  the  melting  of  ice  and  boiling  of  water. 
As  shown  in  the  illustration,  Fig.  6,  these  points  are  marked 
32  and  212  deg.,  respectively,  in  the  Fahrenheit,  and  0  and  100 
deg.,  respectively,  in  the  centigrade  scale.  Thus,  180  deg.  of 


FIG.  6. 


44 


MINE  CASES  AND  VENTILATION 


the  former  correspond  to  100  deg.  of  the  latter;  or  the  ratio  is 
9:5. 


TABLE  SHOWING  CORRESPONDING  VALUES  OF  THE  FAHRENHEIT  SCALE 
FOR  EACH  FIVE  DEGREES  OF  THE  CENTIGRADE  SCALE 


c. 

'  F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

-50 

--58 

200 

392 

450 

842 

700 

1292 

950 

1742 

-45 

-49 

205 

401 

455 

851 

705 

1301 

955 

1751 

-40 

-40 

210 

410 

460 

860 

710 

1310 

960 

1760 

-35 

-31 

215 

419 

465 

869 

715 

1319 

965 

1769 

-30 

-22 

220 

428 

470 

878 

720 

1328 

970 

1778 

-25 

-13 

225 

437 

475 

887 

725 

1337 

975 

1787 

-20 

-  4 

230 

446 

480 

896 

730 

1346 

980 

1796 

-15 

+  5 

235 

455 

485 

905 

735 

1355 

985 

1805 

-10 

14 

240 

464 

490 

914 

740 

1364 

990 

1814 

-  5 

23 

245 

473 

495 

923 

745 

1373 

995 

1823 

0 

32 

250 

482 

500 

932 

750 

1382 

1000 

1832 

+5 

41 

255 

491 

505 

941 

755 

1391 

1005 

1841 

10 

50 

260 

500 

510 

950 

760 

1400 

1010 

1850 

15 

59 

265 

509 

515 

959 

765 

1409 

1015 

1859 

20 

68 

270 

518 

520 

968 

770 

1418 

1020 

1868 

25 

77 

275 

527 

525 

977 

775 

1427 

1025 

1877 

30 

86 

280 

536 

530 

986 

780 

1436 

1030 

1886 

35 

95 

285 

545 

535 

995 

785 

1445 

1035 

1895 

40 

104 

290 

554   540 

1004 

790 

1454 

1040 

1904 

45 

113 

295 

563 

545 

1013 

795 

1463 

1045 

1913 

50 

122 

300 

572 

550 

1022 

800 

1472 

1050 

1922 

55 

131 

305 

581 

555 

1031 

805 

1481 

1055 

1931 

60 

140 

310 

590 

560 

1040 

810 

1490 

1060 

1940 

65 

149 

315 

599 

565 

1049 

815 

1499 

1065 

1949 

70 

158 

320 

608 

570 

1058 

820 

1508 

1070 

1958 

75 

167 

325 

617 

575 

1067 

825 

1517 

1075 

1967 

80 

176 

330 

626 

580 

1076 

830 

1526 

1080 

1976 

85 

185 

335 

635 

585 

1085 

835 

1535 

1085 

1985 

90 

194 

340 

644 

590 

1094 

840 

1544 

1090 

1994 

95 

203 

345 

653 

595 

1103 

845 

1553 

1095 

2003 

HEAT 


45 


c. 

F. 

C. 

F. 

c. 

F. 

C. 

F. 

C. 

F. 

100 

212 

350 

662 

600 

1112 

850 

1562 

1100 

2012 

105 

221 

355 

671 

605 

1121 

855 

1571 

1105 

2021 

110 

230 

360 

680 

610 

1130 

860 

1580 

1110 

2030 

115 

239 

365 

689 

615 

1139 

865 

1589 

1115 

2039 

120 

248 

370 

698 

620 

1148 

870 

1598 

1120 

2048 

125 

257- 

375 

707 

625 

1157 

875 

1607 

1125 

2057 

130 

266 

280 

716 

630 

1166 

880 

1616 

1130 

2066 

135 

275 

385 

725 

635 

1175  !  885 

1625 

1135 

2075 

140 

284 

390 

734 

640 

1184 

890 

1634 

1140 

2084 

145 

293 

395 

743 

645 

1193 

895 

1643 

1145 

2093 

150 

302 

400 

752 

650 

1202 

900 

1652 

1150 

2102 

155 

311 

405 

761 

655 

1211 

905 

1661 

1155 

2111 

160 

320 

410 

770 

660 

1220 

910 

1670 

1160 

2120 

165 

329 

415 

779 

665 

1229 

915 

1679 

1165 

2129 

170 

338 

420 

788 

670 

1238 

920 

1688 

1170 

2138 

175 

347 

425 

797 

675 

1247 

925 

1697 

1175 

2147 

180 

356 

430 

806 

780 

1256 

930 

1706 

1180 

2156 

185 

365 

435 

815 

685 

1265 

935 

1715 

1185 

2165 

190 

374 

440 

824 

690 

1274 

940 

1724 

1190 

2174 

195 

383 

445 

833 

695 

1283 

945 

1733 

1195 

2183 

To  convert  Fahrenheit  (F.)  readings  into  centigrade    (C) 
or  vice  versa,  the  following  formulas  are  useful : 

F  =  %  C  +  32 

C  =  %  (F  -  32) 

Example — (a)  What  are  the  readings  of  the  Fahrenheit  scale  corre- 
sponding to  40°,  and  —  10°  centigrade? 
Solution — 

F  =  %  X  40  +  32  =  104°F. 

F  =  %  (  -  10)  +  32  =  14°F. 

Example — Convert    —  4  F.  and  50  F.  into  centigrade  readings. 
Solution — 

C  =  %  (-  4  -  32)  =  -  20  C. 

C  =  %  (50  -  32)  =  10  C. 

Readings  above  zero  are  plus  (  +  )  and  those  helow  zero  minus  (  — ). 


46  MINE  GASES  AND  VENTILATION 

SOURCES  AND  MEASUREMENT  OF  HEAT 

Sources  of  Heat. — In  a  sense  the  sun  is  the  original  source 
of  most  of  the  heat  of  the  solar  system — in  other  words,  the 
sun  is  the  power  house  of  that  system.  It  may  be  said  that 
much  of  the  terrestrial  life  and  activity  emanates  from  the 
sun.  The  source  of  the  sun's  heat  is  understood  to  be  the 
chemical  and  possibly  electrical  activities  that  are  constantly 
developed  in  its  huge  mass  and  radiating  heat,  light  and  elec- 
trical energy. 

The  same  chemical  and  possibly  electrical  activities  are 
taking  place  to  a  less  degree  in  the  mass  of  the  earth,  creating 
internal  heat.  Both  the  radiated  heat  of  the  sun  and  the 
internal  heat  of  the  earth  are  natural  sources  of  heat. 

Besides  these  natural  or  physical  sources  of  heat,  there 
are  the  mechanical  sources  of  heat,  such  as  friction,  impact 
and  pressure.  These  each  develop  heat  as  the  result  of  force 
applied  mechanically. 

Sensible  Heat. — The  heat  that  is  accompanied  by  a  change 
of  temperature  when  absorbed  or  given  out  by  a  body  is  called 
"sensible  heat,"  because  it  is  manifest  to  the  senses. 

Latent  Heat. — When  matter  passes  from  the  solid  to  the 
liquid  state,  or  from  the  liquid  to  the  gaseous  state,  the 
change  is  always  accompanied  by  the  absorption  of  a  con- 
siderable amount  of  heat,  although  the  temperature  remains 
constant.  The  heat  thus  absorbed  is  called  "latent  heat,"  it 
being  absorbed  in  performing  the  work  of  driving  the  mole- 
cules of  matter  farther  apart  than  they  were  in  the  previous 
state.  This  heat  is  again  given  out  when  the  matter  passes 
from  a  gas  to  a  liquid,  or  from  a  liquid  to  a  solid. 

Chemical  Heat. — Theory  assumes  that  chemical  heat  is  the 
result  of  the  chemical  affinity  of  material  atoms  for  each  other, 
by  which  they  are  drawn  and  held  in  more  or  less  close  con- 
tact and  union.  This  condition  is  in  harmony  with  the  notion 
of  "atomic  heat,"  explained  elsewhere,  and  suggests  the  esti- 
mation of  the  heat  of  formation,  or  heat  of  combination,  as 
the  result  of  chemical  union. 

In  contrast  with  atomic  heat,  molecular  heat  is  akin  to 
specific  heat  and  representative  of  the  heat  capacity  of  a  sub- 
stance, or  the  quantity  of  heat  a  particular  substance  will 


HEAT  47 

absorb,  per  unit  weight,  per  degree  of  rise  in  its  temperature. 
Theory  assumes  that  all  heat  of  any  nature  is  a  vibratory 
state  of  atoms  or  molecules  and,  as  such,  is  convertible  into 
or  created  by  other  forms  of  energy. 

The  molecular  heat  of  a  substance  is  found  by  multiplying 
a  gram-molecule  (page  54)  of  the  substance  by  its  specific  heat. 

Combining  Heat. — All  matter  is  assumed  to  possess  a  cer- 
tain definite  heat  energy  peculiar  to  itself,  which  is  expressed 
in  heat  units,  per  unit  weight  of  substance  and  called  the 
"combining  heat"  of  the  substance. 

Heat  of  Formation. — In  the  combining  of  atoms  to  form 
compound  molecules,  a  neutralization  of  the  energies  of  the 
combining  atoms  causes  either  an  evolution  or  an  absorption 
of  heat,  the  molecule  formed  then  possessing  an  amount  of 
heat  called  "heat  of  formation"  or  "heat  of  combination." 

Heat  Due  to  Friction, — Friction  is  caused  by  one  body  rub- 
bing against  another,  whereby  a  molecular  vibration  is  set  up 
in  the  two  bodies,  as  manifested  by  the  heat  generated. 

Heat  Due  to  Impact. — The  impact  of  one  body  against  an- 
other likewise  sets  up  a  molecular  vibration  in  the  bodies,  which 
is  manifested  by  the  heat  generated. 

Heat  Due  to  Pressure. — Pressure  applied  to  a  body  having 
a  degree  of  elasticity,  or  being  compressible,  forces  the  mole- 
cules of  matter  closer  together,  which  reduces  the  intermo- 
lecular  space  and,  as  a  result,  there  being  no  loss  of  molecular 
energy,  the  speed  of  vibration  is  increased  in  proportion  as  the 
space  is  diminished  arid  heat  is  developed. 

Transformation  of  Heat  Energy. — Heat  energy  of  any  na- 
ture, whether  chemical  or  physical,  is  convertible,  without 
loss,  into  mechanical  energy  measured  in  foot-pounds,  which 
is  the  "mechanical  equivalent  of  heat." 

At  each  change  of  state  in  matter  heat  is  either  absorbed 
and  becomes  latent  in  the  mass,  or  is  given  out  and  becomes 
sensible,  causing  a  rise  of  temperature  in  the  surrounding 
medium.  Heat  is  absorbed  when  a  solid  becomes  a  liquid  or 
a  liquid  becomes  a  gas,  the  change  being  one  in  which  the 
density  of  the  mass  is  made  less.  On  the  other  hand,  heat  is 
given  out  when  a  gas  is  condensed  to  a  liquid  or  a  liquid  to  a 
solid,  the  density  of  the  mass  being  then  increased. 


48  MINE  GASES  AND  VENTILATION 

Heat  of  Fusion. — The  change  from  a  solid  to  a  fluid  state 
is  described  as  "liquefaction"  when  solution  takes  place,  or 
"fusion"  if  the  solid  is  melted.  The  heat  absorbed  in  the 
latter  case  is  called  "heat  of  fusion." 

Liquefaction  may  take  place  as  the  result  of  the  absorp- 
tion of  moisture  from  the  air,  the  substance  dissolving  either 
wholly  or  in  part  in  the  water  absorbed.  Such  a  substance 
is  said  to  be  "deliquescent." 

Solution  takes  place  when  a  solid  disappears  in  a  liquid 
in  which  it  is  immersed.  The  solid  is  "dissolved,"  in  the 
liquid,  which  is  called  the  "solvent." 

In  any  case  of  liquefaction  or  fusion  heat  is  absorbed  and 
becomes  latent  in  the  liquid,  causing  a  seeming  loss  or  dis- 
appearance of  heat.  When  a  solid  is  dissolved  in  a  liquid  the 
liquid  is  cooled  provided  no  chemical  reaction  takes  place, 
which  might  produce  heat. 

Heat  of  Vaporization. — The  formation  of  vapor  or  the 
change  from  a  solid  or  liquid  to  a  gaseous  state  is  known  as 
"vaporization"  and  the  heat  absorbed  and  rendered  latent  in 
the  vapor  is  called  "heat  of  vaporization"  or  frequently  "heat 
of  evaporation,"  especially  when  the  vapor  is  formed  by  boil- 
ing the  liquid. 

Heat  of  Condensation. — When  a  gas  or  vapor  is  condensed 
to  a  liquid  or  a  liquid  is  frozen  or  condensed  to  a  solid  the 
latent  heat  of  the  gas,  vapor  or  liquid  is  given  out  and  appears 
as  sensible  heat,  which  causes  a  rise  of  temperature.  The 
heat  given  out  is  called  "heat  of  condensation"  and  is  exactly 
equal  to  the  heat  of  vaporization  or  the  heat  of  fusion  or 
liquefaction,  as  the  case  may  be. 

Total  Heat  in  a  Body. — By  this  is  meant  the  total  heat 
absorbed  by  a  body  in  a  given  change  of  temperature  or  state. 
For  example,  the  total  heat  in  1  Ib.  of  water,  in  passing  from 
ice  at  32  deg.  F.  to  steam  at  212  deg.  F.  is  as  follows: 

Latent  heat  of  fusion  of  ice,  from  and  at  32°F 144      B.t.u. 

Sensible  heat  absorbed  by  water,  32°  to  212°F 180      B.t.u. 

Latent  heat  of  vaporization,  from  and  at  212°F.  .  .     970.4  B.t.u. 


Total  heat  absorbed.  .  .    1294.4  B.t.u. 


HEAT  49 

The  total  heat  of  steam  at  any  temperature  or  pressure 
is  usually  estimated  from  water  at  32  deg.  F.;  thus  the  total 
heat  in  steam  (water  vapor)  at  212  deg.  F.  is  180  +  970.4  = 
1150.4  B.t.u.  This  is  the  heat  in  steam  at  atmospheric  pres- 
sure at  sea  level  (14.7  Ib.  per  sq.  in.).  When  steam  is  gener- 
ated in  a  boiler,  its  temperature  increases  with  the  pressure. 

Effect  of  Pressure  on  Fusion. — Pressure  acts  to  oppose 
increase  of  volume.  Some  substances,  as  water,  for  example, 
expand  when  passing  from  the  liquid  to  the  solid  state  and 
an  increase  of  pressure  therefore  lowers  the  freezing  point 
of  such  substances.  The  decrease  of  atmospheric  pressure  at 
high  altitudes  facilitates  the  formation  of  ice,  though  to  a 
less  degree  than  other  more  potent  causes. 

On  the  other  hand,  some  substances,  as  wax,  contract  when 
solidifying,  and  an  increase  of  pressure  then  acts  to  raise  the 
freezing  point  or  point  of  solidifying.  In  other  words,  an  in- 
crease of  pressure  acts  to  assist  the  melting  of  wax  and  similar 
substances,  while  it  retards  that  of  ice. 

Melting  Points  of  Substances. — The  melting  point  of  sub- 
stances depends  largely  on  their  purity  and  treatment.  For 
this  reason  different  authorities  often  give  different  values 
for  the  same  substance.  The  table  on  the  following  page 
gives  the  approximate  melting  points  and  the  heat  of 
fusion,  in  British  thermal  units,  per  pound,  for  the 
substances  named. 

Difference  Between  Melting  and  Freezing  Points. — The 
melting  point  of  a  substance  does  not  always  correspond  ex- 
actly with  its  freezing  point,  even  at  the  same  pressure.  The 
melting  point  of  ice  is  more  uniformly  constant  than  the 
freezing  point  of  water,  and  for  this  reason  is  taken  to  indi- 
cate the  zero  of  the  centigrade  scale  (32°F.). 

The  solidification  of  a  liquid  is  generally  accompanied  with 
crystallization,  and  the  formation  of  the  crystals  is  often 
delayed  in  a  quiet  medium,  so  that  the  temperature  of  water 
free  of  air  may  fall  as  low  as  5  deg.  F.  when  perfectly  quiet 
and  not  freeze.  But  if  the  water  at  this  low  temperature  be 
stirred  or  jarred  the  whole  will  instantly  change  to  ice  or 
become  solid. 


50  MINE  GASES  AND  VENTILATION 

MELTING  POINTS  AND  HEATS  OF  FUSION  OF  SUBSTANCES 


Substance 

Melting  point, 
deg.  Fahr. 

Heat  of  fusion, 
B.t.u.  per  Ib. 

Aluminum  
Beeswax  
Copper  
Gold 

1211 
148 
1980 
1947 

138.6 
76.1 

77.4 

Ice  ... 

32 

144  0 

Iron,  cast  (white)  
Iron,  cast  (gray)  

2000 
2400 

41.4 
59.4 

Iron,  wrought  
Lead  
Nickel 

2820 
620 
2600 

9.0 
8  3 

Platinum  
Silver  
Spermaceti 

3100 
1764 
120 

48.6 
37.9 
66  5 

Steel  

2462 

36.0 

Sulphur  
Tallow 

235 

92 

16.2 

Tin 

450 

25  6 

Zinc  

786 

50.4 

To  express  heat  of  fusion  in  calories  per  kilogram: 
B.t.u.  per  Ib.  X  %  =  cal.  per  kg. 

.  Effect  of  Pressure  on  Vaporization. — Pressure  acts  to  re- 
tard vaporization.  An  increase  of  pressure,  therefore,  raises 
the  boiling  point  of  water  and  other  liquids.  For  the  same 
reason  a  decrease  of  pressure  lowers  the  boiling  point  of 
liquids.  At  an  elevation  of  10,000  ft.  above  sea  level,  under 
normal  atmospheric  conditions,  pure  water  boils  at  193  deg. 
F.,  and  at  an  elevation  of  15,000  ft.  the  boiling  point,  for  the 
same  normal  atmospheric  conditions,  is  reduced  to  185  deg.  F. 

Vaporization,  Evaporation,  Betting. — Vaporization  is  a 
general  term  relating  to  the  formation  of  vapor,  or  the  change 
from  a  solid  or  liquid  state  to  a  vaporous  or  gaseous  con- 
dition, without  regard  to  whether  the  change  is  slow  or  rapid. 

The  term  "evaporation"  relates  to  the  slow  vaporizing  of 
a  solid  or  liquid  that  takes  place  at  its  surface  when  the 
latter  is  exposed  to  an  atmosphere  that  is  not  fully  saturated. 


HEAT  51 

The  evaporation  of  a  liquid  may  also  be  caused  by  the  applica- 
tion of  heat. 

The  term  "boiling"  refers  to  the  violent  ebullition  that 
takes  place  throughout  the  mass  of  a  liquid,  caused  by  the 
formation  of  vapor  in  the  liquid  and  its  escape  to  the  surface. 
Boiling  results  from  the  application  of  heat  to  the  liquid,  or 
may  result  from  a  sudden  decrease  of  pressure. 

Boiling  Points  of  Liquids. — A  liquid  boils  when  raised  to 
such  a  temperature  that  the  tension  of  its  vapor  is  equal  to 
the  pressure  at  its  surface.  At  this  point  the  liquid  becomes 
vapor.  The  term  "boiling  point,"  as  commonly  used,  however, 
refers  to  atmospheric  pressure  at  sea  level,  unless  otherwise 
stated.  The  following  table  gives  both  the  freezing  and  the 
boiling  points  of  a  few  liquids  of  interest  in  mining: 

FREEZING  AND  BOILING  POINTS  OF  LIQUIDS 

T  ioiljj  Freezing  Point,  Boiling  Point, 

Deg.  Fahr.  Deg.     Fahr. 

Alcohol  (ethyl) ..'. -202  172 

Ammonia.  .  .  .' —106  140 

Linseed  oil -18  597 

Mercury —38  .       676 

Nitroglycerine 45 

Measurement  of  Heat. — Although  heat,  as  already  ex- 
plained, is  a  condition  of  matter  and  not  a  tangible  quantity,  it 
is  possible  to  measure  its  intensity  or  degree  through  the  effect 
it  produces,  referred  to  certain  established  standards  of  meas- 
urement. The  most  convenient  standard  is  the  heat  energy 
that  will  cause  a  rise  of  one  degree  in  the  temperature  of  a 
unit  weight  of  pure  distilled  water  at  its  point  of  maximum 
density.  This  is  called  a  "heat  unit"  or  "thermal  unit"  and 
is  a  quantity  capable  of  exact  measurement. 

Heat  or  Thermal  Units.— There  are  several  heat  units  in 
common  use,  the  principal  ones  being  the  British  unit  and 
the  French  unit.  A  third  unit  that  is  largely  used  combines 
these  two  units. 

The  British  Thermal  Unit.— The  British  thermal  unit 
(B.t.u.)  is  the  quantity  of  heat  required  to  raise  the  tempera- 


52  MINE  GASES  AND  VENTILATION 

ture  of  1  Ib.  of  pure  distilled  water  at  maximum  density,  1 
deg.  of  the  Fahrenheit  scale. 

The  French  Thermal  Unit  or  Calorie. — This  is  the  quantity 
of  heat  required  to  raise  the  temperature  of  1  kg.  of  pure  dis- 
tilled water  at  maximum  density,  1  deg.  of  the  Centigrade 
scale. 

The  Pound  Calorie. — This  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  1  Ih.  of  pure  distilled  water,  at 
maximum  density,  1  deg.  of  the  Centigrade  scale. 

Conversion  Formulas — 

B.t.u.  X  0.252     =  Calories 

B.t.u.  X      %       =  Pound-calories 

Calories  X  3.968     =  B.t.u. 

Calories  X  2.2046  =  Pound-calories 

Pound-calories  X      %  B.t.u. 

Pound-calories  X  0.4536  =  Calories 
Note. — Since     1  Ib.  (avoirdupois)  =  0.4536  kg.;  and 
1  deg.  (Fahr.)  =  %  deg.  (Cent.), 

1  B.t.u.  =  0.4536  X  %  =  0.252  cal. 
Again,  since       1  kilogram         =  2.2046  Ib.  (avoir.);  and 

1  deg.  (Cent.)  =  '%  deg.  (Fahr.), 
*   1  cal.  =  2.2046  X  H  =  3.968  B.t.u. 

These  simple  calculations  show  the  derivation  of  the  constants  used 
in  the  above  formulas. 

Transmission  of  Heat. — The  condition  known  as  "heat"  is 
transmitted  in  any  one  of  the  three  following  ways:  1.  By 
radiation.  2.  By  conduction.  3.  By  convection. 

Heat  is  radiated  in  straight  lines  in  all  directions  from  its 
source  and  is  then  called  "radiant  heat."  It  is  transmitted 
through  the  vibrations  of  the  ether  that  fills  all  space  and  the 
radiated  heat  is  imparted  in  varying  degree  to  all  matter  in 
its  path.  Heat  so  imparted  to  a  body  is  said  to  be  "absorbed  " 
by  the  body. 

When  heat  travels  through  a  body  the  process  of  transmis- 
sion is  known  as  "conduction."  Heat  thus  spreads  through- 
out the  mass  as  a  solid. 

The  spread  of  heat  in  any  fluid  (liquid  or  gas)  is  through  the 
circulation  caused  by  the  unequal  distribution  of  the  heat. 
This  mode  of  transmission  is  known  as  "convection." 


HEAT  53 

Mechanical  Equivalent  of  Heat. — Since  heat  is  assumed  to 
be  a  form  of  energy,  it  must  be  capable  of  performing  work, 
which  is  expressed  in  foot-pounds.  This  has  given  rise  to 
what  is  properly  called  the  " mechanical  equivalent  of  heat." 
It  is  the  theoretical  amount  of  work  expressed  in  foot-pounds 
or  kilogram-meters  per  unit  of  heat  absorbed. 

The  values  of  the  several  heat  units  are  as  follows: 

Foot-pounds  Kilogram-meters 

1  British  thermal  unit 778  107 . 5 

1  calorie 3087  426 . 8 

1  pound-calorie 1400  193 . 5 

The  reverse  of  these  values  is  as  follows: 

B.t.u.  Calories  Lb.-cal. 

1000  foot-pounds 1 . 285  0 . 324  0 . 714 

100  kilogram-meters 9 . 297  2 . 343  5 . 168 

Atomic  Heat. — -An  important  relation  has  been  found  to 
exist  between  the  atomic  weights  of  the  elements  and  their 
specific  heats.  Dulong  and  Petit  (1819)  found  that  the  spe- 
cific heats  (relative  heat  capacity)  of  most  of  the  solid  ele- 
ments vary  inversely  as  their  atomic  weights,  so  that  the 
product  of  these  two  factors  is  a  constant  quantity  (6.4), 
which  has  been  properly  called  the  "atomic  heat."  Thus,  tak- 
ing the  specific  heats  of  iron,  lead  and  mercury,  respectively, 
as  0.1190,  0.0305  and  0.0333,  gives  the  value  for  the  atomic 
heat  in  each  case  as  follows : 


Iron  

At. 
55. 

wt. 
40 
44 
40 

X 

X 
X 

Sp.  ht. 
0.1190 
0.0305 
0.0333 

=    .6. 
-     6 

=     6 

59 

.27 
61 

At.  ht. 
heat  units, 
heat  units, 
heat  units. 

Lead  
Mercury.  .  . 

.     205. 
.      198. 

The  average  value  for  the  atomic  heat  of  the  elements  may 
be  taken  as  6.4,  though  it  is  sometimes  given  as  low  as  6.25 
(Remsen).  Atomic  heat  may  be  briefly  defined  as  the  heat 
capacity  of  matter  per  unit-weight  atom. 

A  gram-atom  of  any  elementary  substance  is  a  weight  of 
that  substance,  in  grams,  equal  to  the  atomic  weight  of  the 


54  MINE  GASES  AND  VENTILATION 

element.  Thus,  the  atomic  weight  of  iron  being  55.4  (H  =  1), 
a  gram-atom  of  iron  is  55.4  grams  of  that  substance;  and  its 
heat  capacity  is  the  atomic  heat  value  (6.4  heat  units). 

This  average  value  of  atomic  heat  often  assists  the  deter- 
mination of  the  specific  heat  from  the  atomic  weight  of  an 
elementary  substance,  or,  vice  versa,  its  atomic  weight  when 
the  specific  heat  is  known.  For  example,  since  the  heat  ca- 
pacity of  55.4  grm.  of  iron  is  6.4  heat  units,  the  average 
specific  heat  of  iron  is  6.4  -r-  55.4  =  0.1155. 

In  like  manner,  a  gram-molecule  of  any  compound  sub- 
stance is  a  weight  of  that  substance,  in  grams,  equal  to  the 
molecular  weight  of  the  substance. 

Specific  Heat. — Investigation  has  shown  that  the  same 
quantity  of  heat  imparted  to  equal  weights  of  different  sub- 
stances does  not  produce  the  same  rise  of  temperature  in  each 
substance.  Also,  equal  weights  of  different  substances  when 
cooling  give  out  different  quantities  of  heat  for  each  degree 
the  temperature  falls.  These  facts  show  that  different 
substances  have  different  capacities  for  absorbing  and  holding 
heat  as  sensible  heat  causing  a  rise  of  temperature. 

The  " specific  heat"  of  any  substance  is  its  relative  heat 
capacity,  or  its  heat  capacity  referred  to  that  of  an  equal 
weight  of  pure  water.  The  unit  of  heat  is  the  amount  of  heat 
required  to  raise  the  temperature  of  a  unit  weight  of  water 
one  degree.  Therefore,  the  specific  heat  of  a  substance 
being  referred  to  water  expresses  the  heat  units  required  to 
raise  the  temperature  of  a  unit  weight  of  the  substance  one 
degree. 

The  specific  heat  of  a  solid  or  liquid  always  refers  to  the 
heat  per  unit  weight.  The  specific  heat  of  a  gas  may  be  re- 
ferred to  the  unit  weight  or  unit  volume,  as  desired.  The 
specific  heat  of  air  and  gases  is  different  according  as  the  air 
or  gas  is  confined  (constant  volume)  or  is  allowed  to  expand 
(constant  pressure).  The  specific  heat  of  a  gas  for  "equal 
volumes"  is  the  heat  capacity  of  the  gas  referred  to  that  of 
an  equal  volume  of  air  at  the  same  temperature  and  pressure. 

The  following  table  gives  the  specific  heats  of  a  few  of 
the  common  solids  and  liquids  of  interest  in  mining: 


HEAT  55 

SPECIFIC  HEATS  OF  SOLIDS  AND  LIQUIDS 


Substance 

Temperature, 
deg.  Fahr. 

Specific  heat 

Aluminum  

60-1150 

0.2145-0  3077 

Copper. 

32-1650 

0.0933-0  1259 

Iron 

32-1100 

0  1050-0  1989 

Lead  

60-  600 

0.0299-0.0338 

Lead  (at  melting  point,  610°F.)  
Mercury 

610-  680 
32-  500 

0.0356-0.0410 
0  0334-0  0320 

Platinum  
Silver  
Tin 

60-  210 
32-1200 
32-  210 

0.0324 
0.0559-0.0750 
0  0545 

Zinc 

32-  700 

0  0935-0  1220 

The  following  table  gives  the  specific  heats  of  the  common 
mine  gases,  for  equal  weights  at  constant  pressure  and  con- 
stant volume,  and  for  equal  volumes  under  constant  pressure: 

SPECIFIC  HEATS  OF  AIR,  MINE  GASES  AND  VAPORS 


Equal 

weights 

Equal  volumes 

Const,  pres. 

Const,  vol. 

Const,  pres. 

Air  

0  .  2374 

0  .  1689 

0.2374 

Methane     

0.5929 

0.4219 

0.3314 

Olefiant  gas 

0.4040  . 

0  2875 

0  3951 

Carbon  monoxide  
Carbon  dioxide  
Hydrogen  sulphide 

0.2450 
0.2163 
0  2432 

0.1743 
0.1539 
0  1731 

0  .  2369 
0  .  3307 

0  2897 

Oxygen 

0  2175 

0  1548 

0  2405 

Nitrogen  
Hydrogen.     ... 

0.2438 
3  4090 

0.1735 
2  4260 

0.2368 
0  2361 

Water  vapor  
Ammonia 

0.4805 
0  5080 

0.3419 
0  3615 

0.2996 
0  2992 

When  gas,  air  or  vapor  is  free  to  expand  (constant  pres- 
sure)- heat  is  absorbed  and  becomes  latent.  -For  this  reason 
more  heat  is  required  to  produce  the  same  rise  of  tempera- 
ture when  expansion  occurs  than  when  the  volume  remains 


56  MINE  OASES  AND  VENTILATION 

constant,  and  the  specific  heats  in  the  first  column  are  there- 
fore higher  than  those  in  the  second  column  of  the  table 
given  above. 

The  values  given  in  the  first  column  of  this  table  have 
been  determined  by  experiment  directly,  while  those  in  the 
second  column  have  been  derived  from  the  first  by  dividing 
the  latter  by  1.405,  the  ratio  of  the  specific  heat  of  gases  at 
constant  pressure  to  that  at  constant  volume.  Likewise,  the 
values  given  in  the  third  column  have  been  derived  from 
those  in  the  first  by  multiplying  the  latter  by  the  specific 
gravity  of  the  gas  or  vapor  referred  to  air. 

The  specific  heat  of  all  substances  varies  more  or  less  with 
the  temperature  as  appears  in  the  above  table.  In  the  case  of 
gases,  the  increase  per  degree  (Fahr.)  above  zero  is  roughly 
estimated  as  follows :  Air,  nitrogen,  carbon  monoxide,  0.000012; 
oxygen,  0.00001;  carbon  dioxide,  0.00006;  hydrogen,  0.0002; 
and  water  vapor,  0.0001;  etc. 

CHEMISTRY  OF  GASES 

The  chemistry  of  all  matter  treats  of  the  interchange  of 
the  atoms  constituting  molecules,  by  virtue  of  which  inter- 
change the  character  and  nature  of  the  matter  is  wholly 
altered.  In  other  words,  the  matter  is  transformed  and  a. 
new  substance  created  having  properties  that  vary  widely 
from  those  of  the  original  substance. 

Chemical  Reaction. — The  change  that  takes  place  when 
matter  is  thus  transformed  is  a  chemical  change,  and  the 
action  is  described  as  a  " chemical  reaction."  It  assumes  an 
intimate  contact  between  two  unlike  substances,  under  con- 
ditions that  favor  an  interchange  of  atoms.  The  reaction  that 
takes  place  is  the  direct  result  of  different  affinities  of  the 
atoms  for  each  other. 

Chemical  Affinity. — The  theory  of  chemical  change  supposes 
that  all  atoms  constituting  matter  have  various  affinities  or 
degrees  of  attraction  for  each  other.  By  reason  of  this  dif- 
ference in  the  affinities  of  atoms,  an  interchange  may  or  may 
not  occur  when  two  unlike  substances  are  brought  into  inti- 
mate relation  with  each  other,  according  as  the  atoms  of  the 


HEAT  57 

original  substances  possess  a  less  or  a  greater  affinity  for 
each  other  in  their  present  state  or  grouping.  If  the  atoms 
of  one  of  these  substances  possess  a  greater  affinity  for  atoms 
of  the  other  substance  an  interchange  of  atoms  will  take 
place  and  new  substances  will  be  formed  that  will  be  wholly 
different  from  the  original  substances. 

Influence  of  Heat  to  Produce  Chemical  Change. — 'The 
theory  of  heat  assumes  a  wider  separation  of  the  particles  of 
matter  as  the  amount  of  heat  in  a  substance  is  increased. 
Thus,  it  naturally  follows  that  a  higher  temperature  invites  a 
more  intimate  mingling  of  two  different  gases  in  contact  with 
each  other.  This  intermingling  of  the  gaseous  molecules 
greatly  assists  a  chemical  reaction  that  otherwise  would  not 
take  place. 

Examples  of  Chemical  Change. — The  most  common  and  fa- 
miliar examples  of  chemical  change  are  those  due  to  the  strong 
affinity  of  the  oxygen  of  the  air  for  most  other  matter.  The 
resulting  reaction  is  described  as  oxidation.  The  more  familiar 
forms  of  oxidation  are  the  rusting  of  iron  and  some  other 
metals  in  a  damp  atmosphere.  The  action  results  in  the 
"  corrosion "  or  eating  away  of  the  metal  and  the  formation 
of  an  oxide,  which  is  quite  different  in  its  character  and 
properties  from  the  original  metal. 

Combustion. — In  a  general  sense,  any  form  of  oxidation  is 
combustion,  and  the  latter  term  does  not  relate  alone  to  oxida- 
tion, but  describes  generally  any  chemical  reaction  in  which 
one  substance  is  consumed  either  slowly  or  rapidly  by  reason 
of  the  presence  of  another  substance  whose  atoms  possess  an 
affinity  for  those  of  the  first  that  invites  reaction. 

The  substance  consumed  is  termed  the  combustible  and 
the  other  the  supporter  of  the  combustion,  while  the  sub- 
stances produced  are  the  products  of  the  combustion.  The 
products  of  a  combustion  may  be  gaseous,  vaporous  or  solid, 
the  last  named  being  the  ash  of  an  active  combustion. 

Slow  Combustion. — This  term  implies  a  slow  but  continuous 
wasting  away  of  the  substance  consumed,  the  conditions 
being  unfavorable  or  the  affinities  of  the  atoms  being  insuffi- 
cient to  support  a  more  rapid  reaction.  Slow  combustion  is 


58  MINE  GASES  AND  VENTILATION 

characterized  by  the  generation  of  heat  without  the  production 
of  flame. 

Active  or  Rapid  Combustion. — Active  combustion  is  gen- 
erally accompanied  by  the  production  of  flame.  The  same 
amount  of  heat  is  generated  in  less  time,  resulting  in  a  higher 
temperature,  which  in  turn  frequently  modifies  the  products  of 
the  combustion. 

Spontaneous  Combustion. — Under  certain  favorable  condi- 
tions, combustion  may  start  in  a  mass  of  combustible  ma- 
terial without  the  application  of  flame  or  other  exciting  cause. 
This  is  due  to  the  natural  generation  of  heat  within  the  mass, 
owing  to  chemical  reaction  taking  place  between  the  sub- 
stances. The  action  is  explained  as  being  chiefly  due  to  the 
absorption  of  oxygen  from  the  air  by  the  substance,  when  the 
ensuing  oxidation  generates  sufficient  heat  to  ignite  both  the 
gas  produced  by  the  combustion  and  the  material.  The  com- 
bustion, which  is  at  first  slow,  may,  in  time,  develop  actively 
and  inflame  and  consume  the  material. 

Chemical  Symbols. — A  chemical  symbol  is  a  letter  or  letters 
used  to  designate  an  element  or  simple  substance.  The  sym- 
bols of  the  more  common  elements  together  with  their  atomic 
or  specific  weights  have  been  given  in  a  table,  previously. 
The  symbol  written  alone  expresses  a  single  atom  of  the  sub- 
stance; but,  since  an  atom  is  not  conceived  to  exist  alone,  the 
symbol  of  an  element  should  always  be  written  as  a  molecule. 

Symbol  of  a  Molecule. — A  molecule  is  assumed  to  be  the 
smallest  chemical  division  of  matter  that  can  exist  in  a  free 
state.  A  molecule  of  any  simple  or  elementary  substance  is 
assumed  to  contain  two  atoms  only.  Its  symbol  is  expressed 
by  writing  the  symbol  for  that  element  with  a  subscript  (2)  to 
indicate  two  atoms;  thus  for  the  molecule  of  carbon,  write 
C2;  oxygen,  O2;  etc. 

The  molecule  of  a  compound  substance  may  contain  any 
number  of  atoms  and  is  expressed  by  writing  the  symbols  of 
its  elements  each  with  a  subscript  figure  indicating  the  num- 
ber of  atoms  of  that  element  in  the  molecule.  A  single  atom 
of  an  element  is  indicated  by  the  symbol  only,  omitting  the 
subscript  figure. 


HEAT  59 

The  following  examples  will  serve  to  illustrate  the  fact 
that,  while  a  molecule  o.f  any  simple  substance  is  taken  to 
contain  two  atoms  only,  the  molecule  of  a  compound  may 
contain  any  number  of  atoms : 

Substance  Composition  Symbol 

Carbon   monoxide,  carbon,      1  atom;  oxygen,        1  atom    =»  2  atoms;       CO 

Carbon  dioxide,  carbon,      1  atom;  oxygen,        2  atoms  =  3  atoms;        COj 

Ammonia,  nitrogen,  1  atom;  hydrogen,  3  atoms  =  4  atoms;       NHi 

Methane,  carbon,     1  atom;  hydrogen,   4  atoms  =  5  atoms;       CH« 

Olefiant  gas,  carbon,    2  atoms;  hydrogen,  4  atoms  =  6  atoms;       C2H4 

All  these  gaseous  molecules  are  of  equal  size,  though  con- 
taining different  numbers  of  atoms. 

Molecular  Theory  of  Matter. — Chemical  investigations  have 
led  to  the  accepted  conclusion  that  all  matter  is  composed  of 
minute  particles  called  molecules,  the  molecule  being  con- 
sidered the  smallest  division  of  which  the  matter  is  capable 
without  destroying  its  identity. 

Theory  further  assumes  that  the  molecule  is  composed  of 
two  or  more  atoms,  like  or  unlike,  but  bound  together  by  a 
force  of  attraction  for  each  other  known  as  affinity.  Each  of 
these  combined  atoms  represents  an  element  or  a  particular 
kind  of  matter  and  their  combination  as  molecules  diversifies 
matter  and  creates  substances  of  various  nature  and  kind. 

Atomic  Weight. — Atomic  weight  is  simply  relative.  The 
atom  of  each  element  has  a  weight  peculiar  to  that  element, 
referred  to  the  weight  of  the  hydrogen  atom  as  unity. 

Molecular  Weight. — The  molecular  weight  of  a  substance  is 
equal  to  the  sum  of  the  atomic  weights  of  the  elements  of 
which  it  is  composed.  These  elements  combine  in  fixed  pro- 
portions, which  are  determined  by  the  number  of  atoms  that 
saturate  each  other  or  the  " valences"  of  the  elements. 

Valence  or  Valency. — The  valence  of  an  element  is  a  term 
used  to  express  its  combining  power  in  relation  to  the  number 
of  atoms  of  hydrogen  (the  assumed  unit)  or  its  equivalent 
required  to  satisfy  the  affinity.  For  example,  two  atoms  of 
hydrogen  are  required  to  saturate  a  single  atom  of  oxygen, 
and  the  valence  of  hydrogen  being  one,  the  valence  of  oxygen 
is  two.  The  reaction  is  expressed  by  the  chemical  equation 
2H2  +  O2  =  2H2O. 


60  MINE  GASES  AND  VENTILATION 

There  are  many  elements,  however,  that  do  not  unite  with 
hydrogen  and  to  determine  their  valency  it  is  necessary  to 
compare  them  with  other  elements  that  combine  with  them 
and  whose  valence  is  known.  For  this  purpose  the  elements 
oxygen  and  chlorine  are  most  convenient.  The  valence  of 
oxygen,  as  shown  above  is  two.  The  valence  of  chlorine  is 
one,  since  one  atom  of  hydrogen  completely  saturates  one 
atom  of  chlorine. 

H2  +  C12  =  2HC1. 

The  element  calcium  combines  both  with  oxygen  and  with 
chlorine  but  not  with  hydrogen  -alone.  Its  valence  is  two 
as  shown  by  the  following  equations : 

Ca2  +  O2   =  2CaO 
Ca2  +  2C12  =  2CaCl2. 

The  valence  of  most  elements  is  not  absolute  but  changes, 
often  by  two  and  frequently  by  successive  units.  For  example, 
calcium  has  a  valence  of  two  and  four;  gold,  one  and  three; 
copper,  one  and  two;  iron,  two,  three,  four  and  six;  while 
nitrogen  forms  the  following  series  of  oxides: 

N20,  N202,  N203,  N204,  N205. 

Classification  of  Elements  by  Valence. — Owing  to  the 
change  in  valency  exhibited  by  many  elements  it  is  not  pos- 
sible to  make  an  unvarying  classification  in  this  respect.  For 
the  sake  of  convenience,  however,  many  of  the  elements  are 
designated  as  univalent,  bivalent,  trivalent,  quadrivalent,  etc.; 
or  as  monads,  dyads,  triads,  tetrads,  pentads,  hexads,  etc., 
according  as  they  exhibit  valencies  of  one,  two,  three,  four, 
five,  six,  etc.,  in  combining  with  other  elements. 

A  Chemical  Compound. — A  chemical  compound  is  a  sub- 
stance composed  of  molecules  formed  by  the  chemical  union 
of  two  or  more  unlike  atoms.  In  a  chemical  compound  the 
elements  are  always  combined  in  fixed  proportions  and  the 
substance  has  fixed  properties  that  are  always  the  same. 

A  Mechanical  Mixture. — A  mechanical  mixture  is  composed 
of  unlike  substances  mixed  together  in  any  proportion  and 
not  chemically  combined.  The  properties  of  such  a  mixture 


HEAT  61 

vary  with  the  kind  and  proportion  of  the  substances  of  which 
it  is  formed. 

The  atmosphere  is  a  mechanical  mixture  of  oxygen  and 
nitrogen.  Although  the  proportion  of  these  gases  is  practi- 
cally always  the  same  in  pure  air,  the  gases  are  only  mixed 
and  do  not  combine  with  each  other. 

Acids,  Bases  and  Salts. — Chemistry  considers  three  general 
classes  or  conditions  of  matter,  which  make  the  substance 
either  an  acid,  a  base,  or  a  salt. 

Briefly  and  plainly  stated,  an  acid  is  a  substance  that  dis- 
sociates in  aqueous  solution  yielding  hydrogen  ions. 

A  base  is  a  compound  capable  of  reacting  with  an  acid  to 
produce  a  salt.  It  is  an  alkaline  metallic  oxide. 

A  salt  is  a  generally  neutral  compound  formed  by  the 
union  of  an  acid  and  a  base. 

In  general  the  nature  of  an  acid  is  the  direct  opposite  to 
that  of  a  base.  In  combination  they  neutralize  each  other, 
forming  a  neutral  salt  and  water.  The  distinguishing  charac- 
teristics of  all  acids  are:  1.  The  sour  taste.  2.  The  turning  of 
blue  litmus  red.  3.  The  evolution  of  hydrogen  by  contact 
with  a  metal. 

A  number  of  acids  are  formed  by  the  direct  union  of 
hydrogen  with  another  element;  as  hydrochloric  acid  (HC1); 
hydrogen  sulphide  (H2S).  Other  acids  are  formed  by  the 
union  of  two  radicals — the  hydrogen  radical  or  hydroxyl 
(HO)  and  an  acid  radical;  or  they  may  be  considered  as 
the  result  of  the  addition  of  water  (H20)  to  an  anhydrous 
acid  (anhydride). 

In  the  first  instance,  the  formation  is  as  follows: 

Hydrogen  radical  (hydroxyl) 2(HO) 

Acid  radical . .  SO, 


Sulphuric  acid H2SO4 

Or,  again,  the  formation  may  be  regarded  thus: 

Water H2O 

Sulphuric  anhydride SO3 


Sulphuric  acid H2SO4 


62  MINE  GASES  AND  VENTILATION 

Oxides. — Nearly  all  the  elements  unite  with  oxygen  to  form 
oxides,  but  the  affinity  for  oxygen  is  stronger  in  some  cases 
than  in  others.  When  the  affinity  of  the  elements  for  each 
other  is  strong  the  compound  formed  is  more  stable  than 
when  the  affinity  is  weak. 

A  monoxide  is  formed  when  the  molecule  contains  but  one 
atom  of  oxygen;  as  for  example,  carbon  monoxide  (CO). 

A  dioxide  is  formed  when  the  molecule  contains  two  atoms 
of  oxygen,  as  carbon  dioxide  (CO2). 

A  trioxide  contains  three  atoms  of  oxygen. 

Chemical  Change,  Reaction. — Any  interchange  of  atoms 
between  two  substances,  or  a  combination  of  two  unlike  sub- 
stances, by  which  one  or  more  new  substances  are  formed,  is 
a  chemical  change  and  the  process  is  called  a  "chemical 
reaction." 

A  Chemical  Equation. — It  is  a  natural  law  that  no  matter 
is  ever  lost  or  destroyed.  Matter  is  Indestructible.  As  a 
result  of  chemical  change  both  the  form  and  nature  of  the 
matter  may  be  altered — a  solid  may  become  a  liquid  or  gas, 
or  vice  versa;  but  the  weight  of  the  resulting  products  is  the 
same  as  that  of  the  original  substances  that  are  involved  in 
the  reaction. 

Since  there  is  no  change  in  the  weight  of  matter  before 
and  after  chemical  reaction  takes  place,  it  is  possible  to  ex- 
press the  reaction  by  an  equation  showing  the  equality  of 
matter.  This  is  called  a  chemical  equation.  It  is  formed  by 
writing  in  the  first  member  the  chemical  symbols  of  all  the 
substances  entering  or  involved  in  the  reaction,  connecting 
these  together  with  a  plus  (+)  sign.  Likewise,  in  the  second 
member  of  the  equation,  write  the  chemical  symbols  of  the 
several  products  of  the  reaction,  connecting  them  together, 
as  before,  with  a  plus  (+)  sign.  Then  complete  the  equation 
by  writing  the  sign  (  =  )  of  equality  between  the  two 
members. 

For  reasons  that  will  be  better  understood  when  discussing 
molecular  volume,  when  writing  a  chemical  equation  each 
substance  should  be  expressed  by  its  molecular  formula.  This 
means  that  any  elementary  or  simple  substance  as  carbon  (C), 


HEAT  63 

hydrogen  (H)  nitrogen  (N),  etc.,  should  be  expressed  as  a 
molecule;  thus,  C2,  H2,  N2,  etc. 

Illustration. — When  carbon  (C)  is  completely  burned  in  a 
plentiful  supply  of  oxygen  (O)  there  is  produced  carbon  dioxide 
(CO2).  The  reaction  is  expressed  by  the  equation 

C2  +  2O2  =  2CO2 

The  expression  2CO2  should  be  interpreted  to  mean  two  mole- 
cules of  CO2,  each  comprising  one  atom  of  carbon  and  two 
atoms  of  oxygen. 

Observe  there  are  the  same  number  of  atoms  of  carbon  and 
the  same  number  of  oxygen  on  each  side  of  the  equation. 
Not  an  atom  is  lost  in  the  reaction,  although  these  are  grouped 
differently.  In  this  case  the  solid  carbon  unites  with  the 
oxygen  (gas)  and  carbon  dioxide  (gas)  is  produced.  Also,  the 
weight  of  the  carbon  dioxide  is  equal  to  the  sum  of  the  weights 
of  the  carbon  burned  and  the  oxygen  consumed.  There  is 
no  loss  in  weight. 

It  is  important  to  note  that  the  atoms  involved  in  any  re- 
action represent  the  weights  of  the  substances  they  form, 
while  the  molecules  or  molecular  formulas  of  the  several  sub- 
stances represent  their  respective  volumes.  Hence,  when  each 
substance  is  expressed  by  its  molecular  formula  the  chemical 
equation  shows  both  the  relative  weights  of  all  the  substances 
and  the  relative  volumes  of  the  gases. 

In  the  reaction  represented  by  the  above  equation  each 
atom  of  the  carbon  molecule  (C2)  takes  up  two  atoms  of 
oxygen  to  form  the  molecule  of  carbon  dioxide  (CO2),  the 
valence  of  carbon  being  four  and  that  of  oxygen  two.  The 
reaction  in  this  case  is  complete,  the  affinity  of  the  carbon  for 
oxygen  being  fully  satisfied. 

Use  of  Chemical  Equations. — As  previously  stated,  when 
properly  written  a  chemical  equation  shows  both  the  relative 
weights  and  relative  gaseous  volumes  of  each  respective  sub- 
stance involved  in  a  chemical  reaction.  The  relative  weights 
are  indicated  oy  the  molecular  weights  of  the  substances  as 
shown  by  the  completed  equation. 

In  estimating  relative  gaseous  volumes,  the  volume  of  a 


64  MINE  GASES  AND  VENTILATION 

gaseous  atom  is  taken  as  unity  and  since,  as  previously  ex- 
plained, an  elementary  molecule  is  assumed  to  contain  two 
atoms  and  all  gaseous  molecules  at  the  same  temperature  and 
pressure  are  of  equal  size  regardless  of  the  number  of  atoms 
they  contain,  it  follows  that  the  relative* volume  of  all  gaseous 
molecules  is  two. 

Application  of  the  Law  of  Volumes. — The  law  of  molecular 
volume  as  just  explained  finds  important  application  in  cal- 
culating the  volumes  of  gases  that  are  involved  in  a  chemical 
reaction.  While  there  is  never  any  change  in  the  weight  or 
amount  of  matter  due  to  chemical  reaction,  there  frequently 
results  a  change  in  the  volume  of  the  gases  concerned  in  the 
reaction. 

To  illustrate  such  change  of  gaseous  volume,  write  the 
chemical  equation  representing  the  dissociation  of  ammonia 
gas  (NH8)  by  electrolysis,  forming  free  nitrogen  (N)  and 
hydrogen  (H)  gases,  placing  below  each  molecular  formula  its 
relative  or  molecular  volume ;  thus, 

2NH3  =  N2  +  3H2 
Mol.  vol 2  1          3 

It  is  evident  that  two  molecules  of  ammonia  gas,  in  disso- 
ciation, yield  one  molecule  of  nitrogen  and  three  molecules  of 
hydrogen,  making  four  volumes  in  all.  In  other  words,  two 
volumes  become  four.  The  volume  of  the  gases  resulting 
from  the  breaking  up  of  the  molecule  of  ammonia  is,  there- 
fore, double  that  of  the  original  gas. 

There  is  no  chemical  change  of  volume  when  methane  or 
marsh  gas  (CH4)  is  exploded  in  a  plentiful  supply  of  normal 
air,  and  the  methane  is  completely  burned,  forming  only  car- 
bon dioxide  (CO2)  and  water  (H2O).  The  nitrogen  of  the  air 
being  unchanged  it  may  be  omitted  in  writing  the  equation 
expressing  this  reaction,  which  is  as  follows: 

CH4  +  2O2  =  CO2  +  2H2O 
Mol.  vol 1  2  1  2 

The  equation  shows  that  the  complete  combustion  of 
methane  requires  twice  its  volume  of  oxygen;  and  there  is 


HEAT  65 

produced  an  equal  volume  of  carbon  dioxide  and  two  volumes 
of  aqueous  vapor. 

On  the  other  hand,  when  carbon  monoxide  (CO)  is  burned 
in  air,  producing  carbon  dioxide  (CO2),  there  results  a  reduc- 
tion in  volume,  as  shown  by  the  following  equation: 

2CO  +  O2  +  4N2  -  2CO2  +  4N2  . 
Mol.  vol 2  1          4  2  4 

Normal  air  consists  of  practically  one-fifth  oxygen  and 
four-fifths  nitrogen.  The  equation  shows  that  two  volumes 
of  carbon  monoxide,  in  burning,  consume  five  volumes  of  air, 
and  there  remain  two  volumes  of  carbon  dioxide  and  four 
volumes  of  unchanged  nitrogen.  The  seven  volumes  of  the 
original  gas  and  air  are  thus  reduced  to  six  volumes  of  burned 
gases. 

THERMOCHEMISTRY 

Thermochemistry  treats  of  the  heat  changes  that  accom- 
pany all  chemical  reactions.  A  knowledge  of  such  heat 
changes  is  of  the  greatest  importance  in  the  study  of  ex- 
plosive phenomena. 

Heat  Changes. — In. a  chemical  reaction,  when  combination 
takes  place,  the  heat  energy  of  the  compound  or  compounds 
formed  is  the  heat  of  formation  or  combination. 

Chemical  reaction  may  also  be  accompanied  by  dissocia- 
tion or  decomposition  of  a  compound,  its  heat  of  formation 
being  then  heat  of  decomposition,  which  neutralizes  or  is 
neutralized  by  the  heats  of  formation  of  the  products  of  the 
reaction.  The  heat  of  decomposition  of  a  substance  is  always 
equal  to  its  heat  of  formation. 

The  heat  of  elements,  in  a  reaction,  is  always  zero,  there 
being  no  combination  or  dissociation  in  the  element. 

When  the  sum  of  the  heats  of  formation  of  the  products  of 
a  reaction  is  greater  than  the  total  heat  of  decomposition  heat 
is  liberated  and  the  reaction  is  ' l  exothermic ." .  When  the  total 
heat  of  decomposition  is  the  greater,  heat  is  absorbed  and  the 
reaction  is  then  "endothermic." 

5 


66 


MINE  CASE 8  AND  VENTILATION 


Heat  of  Combustion. — This  term  is  generally  applied  to  the 
heat  liberated  in  the  oxidation  of  a  combustible.  The  reaction 
is  exothermic;  and,  in  general, 

TT          f         7      .•  Heat  of  formation       Heat  of  formation 

Heat  of  combustion  =      f         ,  , 

of  products  of  combustible 

The  heat  -of  combustion  of  a  substance,  like  combining 
heat  and  heats  of  formation  or  decomposition,  is  expressed 
in  heat  units,  per  unit  weight  of  substance.  The  following 
table  gives  the  heats  of  combustion  of  some  of  the  more 
important  combustibles  in  mining: 

TABLE  OF  HEATS  OF  COMBUSTION 
(Favre  &  Silbermann) 


Combustible 


Methane,  to  carbon  dioxide  and  water  at  32  deg.  F. .  . . 
Olefiant  gas,  to  carbon  dioxide  and  water  at  32  deg.  F. 

Carbon,  to  carbon  dioxide 

Carbon,  to  carbon  monoxide 

Carbon  monoxide,  to  carbon  dioxide 

Hydrogen,  to  water  at  32  deg.  F 

Hydrogen,  to  steam  at  212  deg.  F .- 

Sulphur,  to  sulphur  dioxide 

Petroleum,  heavy  (sp.  gr.  0.886) 

Petroleum,  light  (sp.  gr.  0.833) 

Coal  (average  values) 

Pennsylvania . 
Pennsylvania 
West  Virginia 
Illinois . 
Ohio 

Kentucky 
Alabama 
Indiana 


Anthracite . . 
Bituminous . 
Bituminous . 
Bituminous . 
Bituminous . 
Bituminous . 
Bituminous. 
Bituminous . 


State 


Fixed  carbon, 
per  cent. 


Heat  of  com- 
bustion, B.t.u. 
per  Ib. 


84.3 

57.0 
65.8 
46.4 
51.5 
50.1 
59.3 
44.3 


23,513 

21,344 

14,544 

4,451 

4,325 

62,032 

51,717 

4,000 

19,000 

18,200 


14,200 
14,900 
14,240 
14,460 
14,400 
12,700 
13,700 
14,140 


The  above  are  average  values  for  each  entire  state,  as 
taken  from  Government  analyses  and  do  not  represent  mining 
districts. 


HEAT  67 

Heat  Calculation. — The  calculation  of  the  heat  of  com- 
bustion from  the  heats  of  combination  of  the  combustible  and 
the  several  products,  formed,  will  be  best  understood  by  a 
practical  illustration  following  the  statement  of  a  few  funda- 
mental principles  that  always  govern  the  operation.  Briefly 
stated  these  are  as  follows : 

1.  No  heat  energy  is  lost,  but  the  heat  of  an  element,  in 
any  reaction,  is  zero,  there  being  neither  combination  nor 
dissociation  possible  in  the  element  as  in  a  compound. 

2.  Total  heat  of  formation  of  products  is  the  positive  (+) 
heat  developed  in  the  reaction. 

3.  Heat  of  decomposition  (same  as  heat  of  formation)  of 
the  combustible  is  the  negative  ( — )  heat  or  the  heat  absorbed 
in  the  reaction. 

4.  The  heat  of  combustion  is  the  net  heat,  or  the  difference 
between  the  total  heat  in  the  products  and  the  heat  in  the 
combustible. 

5.  The  reaction  generates  heat,   or  is  exothermic,   when 
there  is  an  excess  of  positive  (+)  heat. 

6.  The  reaction  absorbs  heat,   or  is  endothermic,   when 
there  is  an  excess  of  negative  ( — )  heat. 

NOTE.— The  chemical  equation  expressing  a  reaction  shows 
the  equivalence  of  weight  of  matter  before  and  after  reaction, 
but  does  not  show  the  thermal  effect. 

A  thermochemical  equation  is  written  by  adding  to  the 
chemical  equation  a  positive  or  a  negative  term  indicating  the 
heat  generated  or  absorbed  in  the  reaction.  This  heat  may 
be  expressed  as  "  gram-calories "  "  kilogram-calories "  or 
"  pound-calories,"  according  as  the  weight  of  the  combustible 
taken  is  a  gram-molecule,  a  kilogram-molecule  or  a  pound- 
molecule.  Or,  the  heat  of  the  reaction  may  be  given  as 
B.t.u.  per  pound,  or  other  denomination.  The  weight-unit 
is  immaterial,  since  the  heat  of  the  reaction  is  always  that 
due  to  the  molecular  weight  of  the  combustible  expressed  in 
the  same  weight-unit. 

The  amount  of  heat  corresponding  to  the  molecular  weight 
of  the  combustible  (expressed  in  any  weight-unit)  is  fre- 
quently called  the  "molecular  heat"  of  the  reaction. 


68 


MINE  GASES  AND  VENTILATION 


The  molecular  heat  of  a  chemical  reaction,  divided  by  the 
molecular  weight  of  the  substance  consumed,  gives  the  heat 
of  the  reaction  per  unit  weight  of  substance,  which  is  the 
heat  of  the  combustion  expressed  in  the  same  denomination  as 
the  weight  of  the  substance. 

Illustration. — The  heat  of  combustion  of  methane  (CH4), 
as  determined  by  Favre  and  Silbermann  (See  Table),  is  23,513 
B.t.u.  per  lb.;  or  23,513  X  %  =  13,063  Ib.-cal.  per  lb.;  or 
13,063  kg.-ca1.  per  kg.  or  grm.-cal.  per  grm  of  the  gas. 

The  molecular  heat  of  this  reaction  is  therefore 
16  X  23,513  =  376,208  B.t.u. 
or  16  X  13,063  =  209,008  cal. 

It  is  observed,  thus,  that  the  molecular  heat,  in  the  com- 
bustion of  methane,  is  the  heat  (B.t.u.)  generated  by  16  lb. 
of  the  gas;  or  the  heat  (Ib.-cal.)  generated  by  the  16  lb.;  or 
the  heat  (kg.-cal.)  due  to  16  kg.;  or  the  heat  (grm.-cal.)  due 
to  16  grm.  of  this  gas.  Different  authorities  have  obtained 
slightly  varying  heat  values  of  the  gases. 

Heats  of  Formation  of  Substances.— The  heats  of  formation 
of  a  few  substances  that  are  of  interest  in  mining  are  given 
in  the  following  table.  The  heats  are  given  as  molecular 
heats  for  convenience  of  substitution  in  equations. 

TABLE  OF  HEATS  OF  FORMATION  OF  SUBSTANCES 


Substance 

Symbol 

Molecular  heats  of  formation 

B.t.u. 

Cal. 

Methane  
Acetylene               .... 

CH4 
C2H2 
C2H4 
C2H6 
CO 
CO2 
H2S 
S02 
H2O 
H2O 
H20 
H2O 

39,060 
98,550 
-20,250 
47,970 
52,200 
174,600 
8,640 
124,668 
128,880 
126,288 
123,048 
105,660 

21,700 
54,750 
-11,250 
26,650 
29,000 
97,000 
4,800 
69,260 
71,600 
70,160 
68,360 
58,700 

Ethene  (olefiant  gas)  
Ethane  
Carbon  monoxide 

Carbon  dioxide  

Hydrogen  sulphide  
Sulphur  dioxide 

Ice  (32°F.)  

Water  (32°F.)  

Water  (212°F  ) 

Steam  (212°F  ) 

HEAT  69 

For  the  most  part,  the  heat  values  in  the  above  table  have 
been  determined  by  experiment,  by  means  of  the  calorimeter. 
The  values  of  the  heats  of  combustion,  as  calculated  from 
these  molecular  heats  of  formation,  by  substitution  in  the 
chemical  equation  expressing  the  reaction,  will  not  be  found 
to  check  the  earlier  determinations  of  Favre  and  Silbermann; 
but  the  variation  is  slight. 

For  example,  writing  the  thermochemical  equation  for  the 
combustion  of  methane,  indicating  the  required  heat  of  com- 
bustion by  x,  we  have 

CH4  +  2  O2  =  CO2        +  2  H2O  -  x 

39,060  +  0       =  174,600  +  2(126,288)  -  x 
x  =  174,600  +  2(126,288)  -  39,060  =  388,116  B.t.u. 
Then,  the  molecular  weight  of  methane  being  16,  the  unit  heat 
of  combustion  is  388,116  -r-  16  =  24,257,  instead  of  23,513 
B.t.u. 

Writing  a  Thermochemical  Equation. — The  thermochemical 
equation  expressing  the  reaction  that  takes  place  and  the 
heat  that  is  generated  in  the  combustion  of  methane  (CH4) 
is  written  thus: 

CH4  +  2O2  =  CO2  +  2H2O  -  388,116  B.t.u. 
Or,  in  the  French  system, 

CH4  +  202  =  C02  +  2H2O  -  215,620  col. 

The  reaction  is  exothermic,  or  generates  heat,  which  is  the 
excess  of  the  heats  of  formation  of  the  products  of  the  com- 
bustion (carbon  dioxide  and  water),  over  the  heat  of  forma- 
tion of  the  combustible  (methane). 

Likewise,  for  the  combustion  of  carbon  to  carbon  dioxide, 
which  generates  14,550  B.t.u.  per  lb.,  or  14,500  X  %  =  8083 
cal.,  the  molecular  heat  of  the  reaction  is   12  X  14,550  = 
174,600  B.t.u.,  or  12  X  8083  =  say  97,000  cal.     The  thermo- 
chemical equation  expressing  this  combustion  is 
C  +  O2  =  CO2  -  174,600  B.t.u. 
or  C  +  O2  =  C02  -     97,000  cal. 

In  these  equations,  the  heat  of  combustion  is  equal  to  the 
heat  of  formation  of  the  product  (carbon  dioxide),  the  heats 
of  the  elements  (carbon  and  oxygen)  being  zero. 


70  MINE  GASES  AND  VENTILATION 

HYGROMETRY 

Hygrometry  is  the  measurement  of  the  amount  of  vapor 
in  the  air,  at  any  given  time.  The  capacity  of  the  air  for 
holding  moisture  varies  with  the  temperature.  For  example, 
at  32  deg.  F.,  a  cubic*  foot  of  air  will  hold  or  has  a  capacity 
of  only  2.13  grains  of  water;  while  at  60  deg.  the  capacity  is 
5.77  gr.  per  cu.  ft.;  at  100  deg.,  19.84  gr.  per  cu.  ft.;  and  at 
212  deg.  F.,  air  fully  saturated  with  moisture  holds  about 
258  gr.  per  cu.  ft. 

Hygrometric  State  of  Air. — Air  absorbs  moisture  from 
bodies  in  contact  with  it,  and  thus  exerts  a  drying  action, 
which  is  of  great  importance  in  mining.  The  absorptive  power 
of  the  air  varies  with  its  degree  of  saturation.  For  example, 
air  at  60  deg.  F.,  containing,  say  2.9  gr.  per  cu.  ft.,  is  only 
about  half  saturated  and  is  then  said  to  contain  50  per  cent, 
of  moisture.  In  this  condition,  the  air  will  readily  absorb 
more  moisture.  The  degree  of  saturation  of  air  is  called  its 
"hygrometric  state." 

Air  is  said  to  be  "dry"  or  "wet,"  according  to  the  degree 
of  its  saturation.  It  is  important  to  observe  that  these  terms 
have  no  reference  to  the  actual  amount  of  vapor  present  in 
a  given  volume  of  air;  but  only  express  how  nearly  the  air  is 
saturated.  For  example,  air  fully  saturated  at  32  deg.  F.  con- 
tains 2.13  gr.  of  moisture  per  cubic  foot  and  is  "wet"  because 
it  is  full  of  water  vapor;  but  if  the  temperature  now  rises  to, 
say  60  deg.,  the  vapor  capacity  of  the  air  is  thereby  increased 
to  5.77  gr.  per  cu.  ft.,  and  its  degree  of  saturation  or  humidity" 
is  then  2.13/5.77  X  100  =  36.9  per  cent.  In  other  words,  the 
air  at  this  temperature  contains  only  36.9  per  cent,  of  its  ca- 
pacity, and  is  therefore  comparatively  speaking,  "dry"  air. 
Owing  to  the  rise  of  temperature,  from  32  to  60  deg.,  the  air 
is  capable  of  absorbing  5.77  —  2.13  =  3.64  gr.  of  moisture  per 
cubic  foot. 

Calculation  of  Weight  of  Moisture  in  Air. — In  order  to  cal- 
culate the  weight  (w),  in  pounds,  of  moisture  contained  in 
one  cubic  foot  of  air,  it  is  necessary  to  know  the  degree  of 
saturation  of  the  air  (c),  its  temperature  (t),  and  the  vapor 
pressure  (pv)  corresponding  to  that  temperature.  This  last 


HEAT  71 

must  be  taken  from  tables  known  as  psychrometric  tables. 
Calling  the  absolute  temperature  T  =  460  +  t,  the  formula  is 

»  =  0.8235^ 

The  constant  0.6235  is  the  specific  gravity  of  water  vapor, 
and  the  constant  0.37  is  the  reciprocal  of  the  weight  of  one 
cubic  foot  of  dry  air,  at  a  temperature  of  1  deg.  F.  (absolute) 
and  a  pressure  of  1  Ib.  per  sq.  in. 

Example. — Calculate  the  weight  of  water  vapor  carried  in 
an  air  current  of  100,000  cu.  ft.  when  the  saturation  is  80  per 
cent,  and  the  temperature  70  deg.  F.,  if  the  vapor  pressure  at 
the  given  temperature  is  tv  =  0.3602  Ib.  per  sq.  in.  (see  Table, 
P.  77). 

Solution. — The  absolute  temperature,  in  this  case,  is  T-  = 
460  +  70  =  530;  and  the  total  weight  of  vapor  is 

100,000  X  0.6235  008g7Xx05336Q02  -  91.62/6. 

How  Humidity  is  Measured. — The  humidity  of  the  air  is 
commonly  measured  by  an  instrument  called  the  "  hygrome- 
ter" or  "psy chrome ter."  This  is  the  "  wet-and-dry-bulb 
hygrometer." 

Other  forms  of  hygrometer  have  been  employed  depending 
on  the  absorption  of  the  moisture  from  the  air  by  certain  hy- 
groscopic substances,  and  dew-point  hygrometers;  but  these 
are  less  simple  and  not  as  portable  as  the  wet-and-dry-bulb 
hygrometer,  which  indicates  the  humidity  by  the  difference 
in  the  reading  of  the  wet-  and  dry-bulb  thermometers. 

The  Hygrometer  or  Psychrometer. — A  neat  and  portable 
form  of  the  wet-and-dry-bulb  hygrometer,  designed  by  the 
Davis  Instrument  Manufacturing  Co.,  is  shown  in  the  Fig.  7. 
Two  delicate  thermometers  are  mounted  on  springs  on  the  in- 
side of  a  light  cylindrical  folding  metallic  case,  the  dry  bulb 
on  the  door  and  the  wet  bulb  in  the  case.  To  the  latter  bulb 
is  attached  a  fine  silk  or  muslin  sack,  which  forms  a  wick  that 
extends  downward  to  the  small  vessel  which  holds  the  water 
that  keeps  this  bulb  wet. 


72 


MINE  GASES  AND  VENTILATION 


Still  another  form  of  this  instrument  is  that  known  as  the 
"  Swing  psychrometer,"  from  the  manner  of  its  use.  As 
shown  in  Fig.  8,  it  consists  of  two  thermometers  mounted 
on  a  metal  support,  which  is  firmly  attached  to  a  handle  on 
which  it  is  arranged  to  swing.  The  left-hand  thermometer 
has  a  dry  bulb  and  its  reading  indicates  the  actual  tempera- 


FIG.  7. 


ture  of  the  air;  while  the  bulb  of  the  right-hand  glass  is 
covered  with  a  sack  that  is  wet  with  water  when  an  observa- 
tion is  to  be  taken. 

Holding  the  handle  in  a  firm  grasp,  the  operator  swings 
the  instrument  so  that  the  metal  support  holding  the  two 
thermometers  rotates  rapidly  on  the  handle  as  an  axis.  The 
swift  movement  accelerates  the  evaporation  from  the  wet 
sack  and  cools  the  bulb  of  that  thermometer,  whose  reading 
enables  the  calculation  of  the  degree  of  saturation  by  differ- 
ence with  the  dry-bulb  reading. 


HEAT 


73 


The  swing  psychrometer  is  a  popular  form  of  the  wet-  and 
dry-bulb  hygrometer,  because  of  its  portability  and  the 
reliability  of  its  indications,  which  are  generally  assumed  to 
be  more  representative  of  the  actual  state  of  the  air,  because 
of  its  movement  when  an  observation  is  being  taken. 


FIG.  8. 

Principle  of  Hygrometer. — Unsaturated  vapors,  like  gases, 
obey  Boyle's  law;  and,  for  any  given  temperature,  the  ratio  of 
the  quantity  or  volume  of  vapoT  is  equal  to  the  pressure  ratio, 
or  the  relative  humidity  (H),  is  expressed  by  the  formula. 

j,  _      Actual  vapor  pressure 
Saturated  vapor  pressure 


74  MINE  GASES  AND  VENTILATION      . 

The  saturated  vapor  pressure  (dry-bulb  temp.)  is  given  in 
the  tables.  The  actual  vapor  pressure,  at  the  time  of  obser- 
vation, is  equal  to  the  saturated  vapor  pressure  of  the  tables, 
for  the  dew-point  temperature,  which,  if  known,  would  make 
the  calculation  easy  by  the  use  of  the  above  formula.  In  the 
use  of  the  wet-and-dry-bulb  hygrometer,  however,  the  rela- 
tive humidity  is  calculated  by  the  formula 


„      P"  '    30V  88 

fl    - 


Pd 

in  which  H  =  relative  humidity;  pw  and  pd  the  respective 
saturated  vapor  pressures  of  the  tables,  for  the  corresponding 
wet-and-dry-bulb  temperatures  tw  and  id',  and  B  the  barometric 
pressure,  in  inches. 

What  the  Wet-and-dry-bulb  Hygrometer  Indicates.  —  The 
wet-and-dry-bulb  hygrometer  shows  the  difference  between 
the  readings  of  the  two  thermometers.  The  dry-bulb  ther- 
mometer, of  course,  indicates  the  actual  temperature  of  the 
air.  The  reading  of  the  wet-bulb  thermometer  is  lowered  by 
the  evaporation  of  the  water  from  the  little  sack  surrounding 
this  bulb,  and  which  is  kept  moist  by  the  water  drawn  up 
through  the  wick  from  the  vessel  below. 

The  difference  of  temperature  indicated  by  these  two  ther- 
mometers depends  on  the  rapidity  of  the  evaporation  of  the 
water  from  the  wet  bulb.  The  evaporation  is  more,  rapid  in 
dry  than  in  wet  air;  and  the  difference  of  reading  is,  thus,  an 
index  or  measure  of  the  degree  of  saturation  of  the  air.  When 
the  ah*  is  fully  saturated  with  moisture  there  is  no  evapora- 
tion from  the  wet  bulb  and  the  readings  of  the  two  thermome- 
ters are  the  same.  The  difference  increases  with  the  dryness 
of  the  air. 

Relative  Humidity  of  Air.  —  -As  previously  explained  the 
relative  humidity  of  air  is  expressed  by  the  ratio  of  the  actual 
vapor  pressure  in  the  air  at  the  time,  to  the  saturated  vapor 
pressure.  The  following  table  gives  the  percentage  of  satu- 
ration or  the  hygrometric  state  of  air  for  various  differences 
of  readings,  at  different  temperatures. 


HEAT 
DIFFERENCE  BETWEEN  DRY  AND  WET  BULBS 


75 


Reading  of 
dry-bulb 
ther.,deg.F 

65 

- 

N 

CO 

'-t 

tQ 

''-• 

i- 

00 

0! 

c 

S 

01 

« 

-r 

IK 

'-r 

t* 

'-. 

N 

co 

•- 

S: 

OS 

•  0 

'?, 

tfi 
i 

?i 

Relative  humidity 

95 

90 

85 

so 

?.-> 

70 

H(l 

r>2 

57 

53 

IS 

11 

10 

:«; 

:?2 

2S 

25 

2:< 

21 

l<) 

17 

15 

13 

12 

10 

66 

95 

90 

85 

so 

76 

71 

66 

62 

58 

53 

I!) 

45 

11 

:57 

33 

2'.) 

2(1 

21 

22 

20 

18 

17 

15 

1H 

11 

67 

95 

90 

85 

so 

7(1 

71 

87 

62 

5s 

54 

.-,() 

1(1 

12 

MS 

34 

:«) 

27 

25 

2:i 

21 

20 

IS 

1(1 

15 

13 

68 

95 

90 

85 

81 

7C, 

71' 

67 

63 

.v.» 

.I,-) 

51 

17 

}:•! 

:•!«) 

35 

:>1 

2S 

2(1 

2-1 

2,'{ 

21 

19 

17 

1(1 

14 

69 

95 

90 

86 

81 

77 

72 

68 

6-1 

5<> 

55 

5] 

17 

11 

10 

36 

32 

29 

27 

25 

21 

22 

20 

19 

17 

!5 

70 

95 

90 
90 

86 

81 

77 

72 

(is 

(11 

(10 

r,(i 

52 

IS 

11 

10 

:57 

:n 

:«) 

28 

2(1 

25 

23 

21 

20 

IS 

17 

71 

95 

86 

S2 

77 

7:i 

(1<) 

M 

(10 

r,d 

53 

10 

15 

11 

:<s 

:<l 

:u 

20 

27 

2(1 

21 

22 

21 

11> 

IS 

72 

95 

91 

86 

S2 

7S 

7:< 

fl'.) 

115 

61 

57 

53 

1'.) 

Ml 

12 

:«» 

:i5 

:<2 

:«> 

2S 

27 

25 

2:< 

22 

20 

1!) 

73 

95 

91* 

86 

S2 

7S 

T.\ 

(19 

(i,-, 

61 

58 

54 

.',() 

46 

1:5 

10 

:{6 

:w 

31 

29 

2S 

2(1 

21 

215 

21 

20 

74 

95 

91 

86 

82 

78 

74 

70 

(1(1 

(12 

5s 

54 

51 

17 

11 

40 

37 

:M 

:{2 

30 

2<) 

27 

25 

21 

22 

21 

75 

96 

91 

87 

82 

78 

71 

70 

66 

<;:•! 

59 

55 

51 

48 

11 

41 

38 

:M 

:{:< 

:n 

:«» 

2S 

2(1 

25 

1W 

22 

76 

96 

91 

87 

83 

7S 

71 

70 

(17 

63 

59 

55 

:,2 

•is 

15 

12 

:{.s 

:15 

:i4 

\V2 

:<o 

2!) 

27 

2(1 

21 

2)5 

77 

96 

91 

87 

s:< 

79 

7f, 

71 

(17 

6.S 

60 

56 

r,2 

IS) 

id 

12 

:w 

:«; 

34 

:u 

31 

••».) 

2S 

27 

25 

21 

To  use  the  table,  find  the  observed  temperature  of  the  air, 
in  the  left-hand  column,  and  the  difference  of  the  observed 
readings  of  the  wet-  and  dry-bulb  thermometers,  at  the  top 
of  the  table;  the  corresponding  number  in  the  table  is  the 
percentage  of  saturation  which  expresses  the  degree  of  humid- 
ity of  the  air.  For  example,  if  the  dry-bulb  temperature  is 
70  deg.  and  the  wet-bulb  64  deg.  F.  the  difference  of  readings 
is  6  deg.  and  the  corresponding  humidity  as  taken  from  the 
above  table  is  72  per  cent. 

Actual  Vapor  Pressure. — The  pressures  given  in  the  table 
below  are  the  pressures  the  vapor  exerts  when  the  space  it 
occupies  is  fully  saturated;  they  are  called  the  " saturated 
vapor  pressures."  When  the  weight  of  vapor  in  the  air  is  not 
sufficient  for  saturation  the  vapor  pressure  will  be  exactly  pro- 
portional to  the  degree  of  saturation.  For  example,  if  50  per 
cent,  of  moisture  is  present  or  the  air  only  half  saturated,  at, 
say  70°F.,  the  " actual  vapor  pressure,"  as  it  is  called,  is  one- 
half  of  the  saturated  vapor  pressure,  in  the  table  given  later; 
or  Y^  X  0.3602  =  0.1801  Ib.  per  sq.  in. 

To  calculate  the  actual  vapor  pressure  from  the  difference 
of  the  wet-  and  dry-bulb  temperatures  (t<*  —  tw)  and  the 


76  MINE  GASES  AND  VENTILATION 

barometric  pressure  (B),  in  inches  of  mercury,  first  find  the 
saturated  vapor  pressure  (pw),  in  inches  of  mercury,  corre- 
sponding to  the  wet-bulb  temperature  (£„,),  from  the  table; 
and  substitute  this  and  the  given  values  in  the  formula 

Actual  vapor  pressure  at  temperature  td  =  pw  —  ™(  docT^  ) 

oU  \      oo       / 

Example.  —  Find  the  actual  vapor  pressure  when  the  dry  bulb  reads 
60°  and  the  wet  bulb  54°F.,  the  barometric  pressure  being  B  =  30  in., 
and  the  saturated  vapor  pressure  for  the  wet-bulb  temperature  (54°F.) 
being  0.4178  in.  of  mercury. 

Solution.  — 


Pv  =  0.4178  -  =  0.3497  in.  of  mercury 

Since  the  saturated  vapor  pressure  (see  table)  for  the  dry-bulb  tem- 
perature (60°F.)  is  0.5183  in.,  the  relative  humidity  in  the  above  ex- 
ample is 

TT       P*  ^    inn       0.3497  X  100       __  . 
H=pdXl™=     -05183"     =  b7-4  *""•«** 

The  Dew  Point.—  What  is  called  the  "dew  point,"  in  hy- 
grometry,  is  the  temperature  below  which  the  moisture  con- 
tained in  the  air  begins  to  be  deposited.  For  example,  the 
weight  of  moisture,  in  grains  per  cubic  foot,  contained  in  the 
air,  in  the  above  example  is  (1  Ib.  =  7000  grs.) 


7000  X  0.6235  -  3.9  „.  per  cu.  ft. 


The  temperature  at  which  this  weight  of  moisture  will 
fully  saturate  a  cubic  foot  of  air  is  the  dew  point,  because 
the  slightest  fall  of  temperature  below  that  point  will  cause 
a  deposition  of  moisture  from  the  air. 

The  dew-point  temperature  is  ascertained,  in  any  given 
case,  by  first  calculating  the  actual  vapor  pressure  of  the 
moisture  in  the  air,  as  in  the  above  example;  and  then,  by 
referring  to  the  table  of  saturated  vapor  pressures,  find  the 
temperature  orresponding  to  that  vapor  pressure.  This  is 
true,  because,  as  previously  stated,  the  actual  vapor  pressure, 
at  any  given  time,  is  equal  to  the  saturated  vapor  pressure 
for  the  dew-point  temperature.  Thus,  the  actual  vapor  pres- 
sure for  dry  bulb  60°  and  wet  bulb  54°  was  found  to  be  0.3497  in., 
which  corresponds  to  a  saturated  vapor  pressure  or  dew  point 
of  about  49  deg.  F. 


HEAT 


77 


TABLE  SHOWING  SATURATED  VAPOR  PRESSURES  FOR  DIFFERENT 
TEMPERATURES 


Degrees, 
Fahr 

Barometric 
pressure, 
mercury 
(32°F.)  in. 

Pressure, 
pounds  per 
square  inch 

! 

Degrees, 
Fahr 

Barometric 
pressure, 
mercury 
(32°F.)  in. 

Pressure, 
pounds  per 
square  inch 

-30                0.0099 

0.0049 

70 

0.7335 

0  .  3602 

-20                0.0168 

0.0082 

71 

0.7587 

0.3726 

-10               0.0276         0.0136 

72 

0.7848 

0.3854 

0                0.0439 

0.0216 

73 

0.8116 

0.3986 

5               0.0551 

0.0271 

74 

0.8393 

0.4122 

10               0.0691 

0.0339 

75 

0.8678 

0  .  4262 

15               0.0865 

0.0425 

76 

0.8972 

0.4406 

20               0.1074 

0.0527 

77 

0.9275 

0.4555 

26 

0.1397 

0.0686 

78 

0.9587 

0  .  4708 

32 

0.1815 

0.0891 

79 

0.9906 

0.4865 

34 

0.1961 

0.0963 

80 

1.024 

0.5027 

36 

0.2122 

0.1042 

81 

1.058 

0.5194 

37 

0.2205 

0.1083 

82 

1.092 

0.5365 

38 

0.2293 

0.1126 

83 

1.128 

0  .  5542 

39 

9.  .2382 

0.1170 

84 

1.165 

0.5723 

40 

0*2476 

0.1216 

85 

1.203 

0.5910 

41 

0.2574 

0.1264 

86 

1.243 

0.6102 

42 

0.2674 

0.1313 

87 

1.283 

0.6299 

43 

0.2777 

0.1364 

88 

1.324 

0.6502 

44 

0.2885 

0.1417 

89 

1.367 

0.6711 

45 

0.2995 

0.1471 

90 

1.410 

0.6925 

46 

0.3111 

0.1528 

95 

1.647 

0.8090 

47 

0.3229 

0.1586 

100 

1.918 

0.9421 

48 

0.3352  . 

0.1646 

105 

2.227 

1.0938 

49 

0.3478 

0.1708 

110 

2.578 

1  .  2663 

50 

0.3610 

0.1773 

115 

2.977 

1.4618 

51 

0.3745 

0.1839 

120 

3.427 

1.6828 

52 

0.3885 

0.1908 

125 

3.934 

1.9318 

53 

0.4030 

0.1979 

130 

4.504 

2.2119 

54 

0.4178 

0.2052 

135 

5.144 

2.5261 

55 

0.4333 

0.2128 

140 

5.859 

2.8774 

56 

0.4492 

0.2206 

145 

6.658 

3.2696 

57 

0.4657 

0.2287. 

150 

7.547 

3.7063 

58 

0  .  4826 

0  .  2370 

155 

8.535 

4.1914 

59 

0.5001 

0  .  2456 

160 

9.630 

4.7292 

60 

0.5183 

0.2545 

165 

10.841 

5.324 

61 

0.5370 

0  .  2637 

170 

12.179 

5.981 

62 

0.5561 

0.2731 

175 

13.651 

6.704 

63 

0.5760 

0.2829 

180 

15.272 

7.500 

64 

0.5964 

0.2929 

185 

17  .  050 

8.373 

65 

0.6176 

0.3033 

190 

18.954 

9.330 

66 

0.6394 

0.3140 

195 

21.130 

10.377 

67 

0.6618 

0.3250 

200 

23  .  457 

11.520 

68 

0.6850 

0.3364 

205 

25.993 

12.765 

69 

0.7086 

0.3481 

212 

29.925 

14.696 

78  MINE  GASES  AND  VENTILATION 

Caution.  —  It  is  absolutely  necessary  in  the  use  of  such 
formulas  as  embrace  terms  or  constants  of  a  given  denomi- 
nation to  use  only  values  of  that  denomination.  For  ex- 
ample, the  formula  for  finding  the  weight  of  moisture  that 
will  saturate  a  cubic  foot  of  air  at  a  temperature  of  t  degrees,  is 

' 


This  is  recognized  as  being  derived  from  the  formula  previ- 
ously given  (p.  71)  to  find  the  weight  of  a  cubic  foot  of  dry 
air  at  a  pressure  p  and  temperature  /,  by  substituting  for  the 
atmospheric  pressure  p  (Ib.  per  sq.  in.),  the  saturated  vapor 
pressure  for  pv  (Ib.  per  sq.  in.);  and  multiplying  the  formula 
by  the  specific  gravity  of  water  vapor  (0.6235)  referred  to  air. 

In  these  formulas,  the  pressure  must  always  be  expressed 
in  pounds  per  square  inch,  because  the  constant  0.37  is  in 
that  denomination;  and  the  temperature  must  be  given  in 
Fahrenheit  degrees,  for  a  like  reason.  Also,  the  weight  will 
be  found  in  pounds  per  cubic  foot  and,  if  desired  in  grains  per 
cubic  foot,  must  be  multiplied  by  7000,  as  there  are  7000  gr. 
in  a  pound  (avdp.). 

On  the  other  hand,  the  formulas  given  for  Calculating  the 
relative  humidity  of  the  air,  or  the  actual  vapor  pressure 
contain  the  constant  88,  which  is  based  on  barometric  pres- 
sure (in.  of  mercury)  and  Fahrenheit  temperatures.  The 
constant  88  is  used  for  all  temperatures  above  32  deg.,  and  96 
for  any  temperature  below  32  deg. 

The  table  of  saturated  vapor  pressures,  on  the  preceding 
page,  gives  the  pressure  or  tension  of  water  vapor  for  differ- 
ent temperatures  (Fahr.  scale),  from  —30  deg.  to  212  deg. 
The  pressures  are  given  both  in  inches  of  mercury  and  pounds 
per  square  inch. 

Example.  —  Find  the  actual  vapor  pressure,  the  relative  humidity, 
dew  point  and  weight  of  moisture  present,  in  grains  per  cubic  foot,  when 
the  readings  of  the  dry-  and  wet-bulb  thermometers  are  62  deg.  and  54 
deg.  F.,  respectively,  and  the  barometric  pressure  is  28.2  in. 

Solution.  —  The  actual  vapor  pressure,  in  this  case,  as  calculated  from 
the  saturated  vapor  pressure  corresponding  to  the  wet-bulb  reading 
(pM  =  0.4178  in.),  is 

,  =  0.4178  - 


HEAT  79 

The  saturated  vapor  pressure  for  the  given  temperature 
(see  Table)  is  pQ2  =  0.5561  in.  and  the  relative  humidity, 


The  dew-point  temperature  corresponding  to  a  saturated 
vapor  pressure  of  0.3323  (see  Table)  is  47.7  deg.  F. 

The  actual  weight  of  vapor  the  saturated  vapor  pressure 
corresponding  to  the  dry-bulb  temperature  62  deg.  F.  (see 
Table)  being  0.2731  Ib.  per  sq.  in.,  is 


7000  X  0.6235  -  3.6  gr.  per  cu.  ft. 


Dry  and  Wet  Air  Compared.  —  Strange  as  it  may  at  first 
appear,  wet  air  is  lighter  than  dry  air,  volume  for  volume. 
This  is  because  the  water  vapor  in  the  air  is  much  lighter 
than  the  same  volume  of  air  which  it  displaces.  The  specific 
gravity  of  water  vapor  referred  to  air  as  a  standard  or  unity 
is  0.6235. 

The  weights,  per  cubic  foot,  of  water  vapor  and  dry,  partly- 
saturated  and  fully-saturated  air,  respectively,  are  calculated 
by  the  following  formulas  : 

Water  vapor,  w  =  0.6235  —^  (1) 

Dry  air,  .w=  „  (2) 


Air  partly  saturated,  w  =  —         '       —  —  (3) 


pa  —     .r 
Air  fully  saturated,     w  =  -  -Q  (4) 


w    =  weight  (Ib.  per  cu.  ft.) 

c     =  degree  of  saturation,  expressed  as  a  decimal 

pa  =  atmospheric  pressure  (Ib.  per  sq.  in.) 

pv  =  saturated-vapor  pressure  (Ib.  per  sq.  in.) 

T  =  absolute  temperature  (deg.  Fahr.) 

It  is  readily  seen,  from  Formulas  2,  3  and  4,  that  perfectly 
dry  air  is  always  heavier  than  air  containing  water  vapor, 
and  that  the  weight  of  air  decreases  as  its  degree  of  satura- 
tion increases.  The  weight  of  moisture  in  air  is  usually 


80  MINE  GASES  AND  VENTILATION 

estimated  in  grains  instead  of  pounds,  per  cubic  foot,  and  it 
is  necessary  to  multiply  the  results  obtained  from  the  above 
formulas  by  7000  (1  Ib.  =  7000  gr.). 

The  same  formulas  expressing  the  atmospheric  pressure 
and  the  vapor  pressure  in  inches  of  barometer  B,  instead  of 
pounds  per  square  inch,  are  as  follows  : 

Q.82757cpv 
Water  vapor,  w  --        —jr~  (5) 

1.32735 
Dry  air,  w  =  -  ——  (6) 


1 

Air  partly  saturated,  w  =          ~  (B  -  0.3765cp,)  (7) 


Air  fully  saturated,      w  =  -r     (B  -  0.3765pv)  (8) 

It  is  evident  that  when  air  is  fully  saturated,  c  =  1,  and 
disappears  from  the  formula.  The  values  of  pv  are  given 
in  a  preceding  table,  in  pounds  per  square  inch  and  inches 
of  mercury. 

Formula  3  is  obtained  by  the  addition  of  Formulas  1  and 
2,  making  pa  =  pa  —  cpv;  and  Formula  5  is  derived  from 
Formula  1,  by  reducing  the  pressure  (Ib.  per  sq.  in.)  to 
pressure  (in.  barom.),  since  1  in.  barom.  =  0.4911  Ib.  per  sq. 
in.  and  (0.6235  X  0.4911)  ^  0.37  =  0.82757.  But  the  value 
of  pv,  in  Formulas  5,  7,  8,  must  be  given  in  inches  of 
barometer,  instead  of  pounds  per  square  inch  as  in  Formulas 
1,  3,  4. 

Important.  —  Properly  speaking,  a  vapor  does  not  saturate 
the  air,  but  the  space  it  occupies;  since,  for  any  given  tem- 
perature, the  same  weight  of  vapor  serves  to  fill  a  given 
space  whether  that  space  is  full  or  void  of  air.  Commonly 
speaking,  vapor  is  said  to  be  saturated  or  unsaturated  ac- 
cording as  the  space  it  occupies  is  saturated  or  otherwise. 

Laws  of  Vapors.  —  The  following  laws  express  the  chief 
characteristics  of  vapors: 

1.  Vaporization  takes  place  at  the  surface  of  all  volatile 
liquids,  at  all  temperatures,  till  the  space  surrounding  the 
liquid  is  saturated  or  the  critical  temperature  is  reached. 


HEAT 


81 


2.  Vapor  pressure  (different  for  different  vapors)  depends 
on  the  temperature  and  the  degree  of  saturation. 

3.  For  any  given  temperature,   the   weight   and   pressure 
of  a  vapor  saturating  a  given  space  is  the  same  whether  that 
space  is  full  or  void  of  air  or  other  gas. 

4.  Saturated  vapor  pressures  increase  with  the  tempera- 
ture and  when  equal  to  the  pressure  above  the  liquid  vaporiz- 
ing, the  ebullition  of  the  liquid  begins,  which  marks  the  boiling 
point  of  the  liquid  for  that  pressure. 


K>090   SO     70      60 


20    25    30     35    40    45      50     55    60     65     70     75     60    .65     90     95    100     105 

DRY-BULB    TEMPERATURES  (  DEG.  FAHR.) 

FIG.   9. 


5.  In  a  confined  space,  a  further  addition  of  heat  to  the 
liquid  causes  a  rise  of  both  temperature  and  vapor  pressure 
till  an  equilibrium  of  densities  of  the  liquid  and  vapor  stops 
further  vaporization  and  marks  the  so-called  "critical  tem- 
perature "  for  that  liquid. 

The  diagram,  Fig.  9,  is  useful  in  showing  at  a  glance  the 
weight  of  water  vapor  that  will  saturate  a  cubic  foot  of 
space  at  any  temperature  from  20  to  105  deg.  F.  and  the 


82  MINE  GASES  AND  VENTILATION 

degree  of  humidity  for  different  dry-  and  wet-bulb  readings 
of  the  psychrometer. 

STEAM 

Steam  is  the  vapor  of  water  formed  at  any  temperature 
at  or  above  the  boiling  point  of  the  water.  It  is  a  certain 
vaporized  or  gaseous  state  of  water.  Water  vaporizing  below 
its  boiling  point  forms  vapor  but  not  steam.  Thus,  while  all 
steam  is  vapor,  correctly  speaking,  all  vapor  is  not  steam. 

Steam  in  its  natural  state  or  when  saturating  a  given  space, 
has  a  temperature  corresponding  to  the  pressure  it  supports. 
This  will  be  more  clearly  understood  by  taking  an  example  of  a 
given  volume  of  steam  in  contact  with  the  water  from  which 
it  was  formed.  For  instance,  the  steam  in  a  steam  boiler, 
at  a  pressure  of  65  Ib.  gage  (sea  level)  or,  say  80  Ib.  absolute, 
has  a  temperature  of  312  deg.  F.  But  any  increase  of  pressure 
will  be  accompanied  with  a  corresponding  increase  in  its  tem- 
perature, so  that,  at  a  pressure  of  155  Ib.  absolute,  the  tempera- 
ture of  the  steam  will  have  increased  to  361  deg.  F. 

Again,  assuming  a  given  volume  of  steam  in  contact  with  the 
water  from  which  it  was  formed,  such  steam  can  neither  be 
compressed  nor  expanded  without  a  corresponding  change 
taking  place  in  its  temperature.  For  example,  for  the  same 
temperature,  any  increase  of  pressure  would  cause  some  of  the 
steam  to  condense,  while  a  decrease  of  pressure  would  cause 
more  steam  to  form,  as  the  water  would  vaporize  under  the 
decreased  pressure.  Thus,  the  space  above  the  water  is 
always  saturated  by  a  weight  of  steam  corresponding  to  the 
temperature,  which  is  fixed  for  any  given  pressure. 

Saturated  Steam. — Saturated  steam  may  be  defined  as 
steam  in  contact  with  water.  From  the  foregoing,  it  will  be 
understood  that  saturated  steam  is  in  its  natural  state,  having 
a  temperature  corresponding  to  its  pressure.  Saturated 
steam  may  be  either  dry  or  wet,  according  as  it  does  or  does 
not  hold  any  entrained  water.  The  density  of  dry  saturated 
steam  is  always  the  same  for  the  same  temperature. 

Superheated  Steam. — When  steam  is  not  in  contact  with 
water,  any  addition  of  heat  causes  an  increase  in  both 


HEAT 


83 


temperature  and  pressure,  the  pressure  increasing  with  the 
absolute  temperature.  The  steam  is  no  longer  saturated, 
and  is  said  to  be  " superheated."  Superheated  steam  is 
always  dry. 

Unlike  saturated  steam,  superheated  steam  follows  the  laws 
of  a  perfect  gas.  For  a  constant  volume,  its  pressure  increases 
with  the  absolute  temperature;  and,  for  a  constant  tempera- 
ture, the  pressure  increases  inversely  as  its  volume.  Steam  is 
superheated,  therefore,  whenever  its  temperature  exceeds  that 
of  saturated  steam,  for  any  given  pressure. 


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FlG.  10. 

Steam  Tables. — The  table,  in  the  following  pages,  gives  the 
temperature,  specific  volume,  heat  of  the  liquid  above  32  deg. 
F.,  latent  heat  of  evaporation,  and  the  total  heat  in  the  steam, 
for  different  absolute  pressures,  as  taken  from  Marks  &  Davis 
Steam  Tables,  which  are  the  generally  accepted  values,  today. 
The  diagram,  Fig.  10,  was  compiled  by  J.  T.  Beard,  Jr.  from 
the  same  source,  and  will  be  found  convenient  for  use  in 
connection  with  the  tables. 


84 


MINE  CASES  AND  VENTILATION 


PRESSURE  TABLE  FOR  DRY  SATURATED  STEAM 

(Condensed  from  Marks  and  Davis,  by  Permission) 


Absolute 
pressure, 
Ib.  per  sq.  in. 

Temp., 
deg.  F. 

Sp.  vol., 
cu.  ft.  per  Ib. 

Heat  of 
the  liquid 
B.t.u. 

Latent  heat 
of  evap. 
B.t.u. 

Total  heat 
of  steam 
B.t.u. 

P 

t 

v  or  s 

h  or  q 

/  or  r 

h 

1 

101.83 

333.0 

69.8 

1034  .  6 

1104.4 

2 

126.15 

173.5 

94.0 

1021.0 

1115.0 

3 

141.52 

118.5 

109.4 

1012.3      1121.6 

4 

153.01 

90.5 

120.9 

1005.7 

1126.5 

5 

162.28 

73.33 

130.1 

1000.3 

1130.5 

6 

170.06 

61.89 

137.9 

995.8 

1133.7 

7 

176.85 

53.56 

144.7 

991.8      1136.5 

8 

182.86 

47.27 

150.8 

988.2      1139.0 

9 

188.27 

42.36 

156.2 

985.0      1141.1 

10 

193  .  22 

38.38 

161.1 

982.0 

1143.1 

11 

197.75 

35.10 

165.7 

979.2      1144.9 

12 

201.96 

32.36 

169.9 

976.6      1146.5 

13 

205  .  87 

30.03 

173.8 

974.2      1148.0 

14 

209.55 

28.02 

177.5 

971.9 

1149.4 

15 

213.0 

26.27 

181.0 

969.7 

1150.7 

16 

216.3 

24.79 

184  .  4 

967.6 

1152.0 

17 

219.4 

23.38 

187.5 

965.6 

1153.1 

18 

222.4 

22.16 

190.5 

963.7 

1154.2 

19 

225.2 

21.07 

193.4 

961.8 

1155.2 

20 

228.0 

20.08 

196.1 

960.0 

1156.2 

21 

230.6 

19.18 

198.8 

958.3 

1157.1 

22 

233.1 

18.37 

201.3 

956.7 

1158.0 

23 

235.5 

17.62 

203.8 

955.1 

1158.8 

24 

237.8 

16.93 

206.1 

953.5 

1159.6 

25 

240.1 

16.30 

208.4 

952.0 

1160.4 

26 

242.2 

15.72 

210.6 

950.6 

1161.2 

27 

244.4 

15.18 

212.7 

949.2 

1161.9 

28 

246.4 

14.67 

214.8 

947.8 

1162.6 

29 

248.4 

14.19 

216.8 

946.4 

1163.2 

30 

250.3 

13.74 

218.8 

945.1 

1163.9 

31 

252.2 

13.32 

220.7 

943.8 

1164.5 

32 

254.1 

12.93 

222.6 

942.5 

1165.1 

33 

255.8 

12.57 

224.4 

941.3 

1165.7 

34 

257.6 

12.22 

226.2 

940.1 

1166.3 

35 

259.3 

11.89 

227.9 

938.9 

1166.8 

36 

261.0 

11.58 

229.6 

937.7 

1167.3 

37 

262.6 

11.29 

231.3 

936.6 

1167.8 

38 

264.2 

11.01 

232.9 

935.5 

1168.4 

39 

265.8 

10.74 

234.5 

934.4 

1168.9 

40 

267.3 

10.49 

236.1 

933  .  3 

1169.4 

41 

268.7 

10.25 

237.6 

932.2 

1169.8 

42 

270.2 

10.02 

239.1 

931.2 

1170.3 

43 

271.7 

9.80 

240.5 

930  .  2 

1170.7 

44 

273.1 

9.59 

242.0 

929.2 

1171.2 

45 

274.5 

9.39 

243.4 

928.2 

1171.6 

46 

275.8 

9.20 

244.8 

927.2 

1172.0 

47 

277.2 

9.02 

246.1 

926.3 

1172.4 

48 

278.5 

8.84 

247.5 

925.3 

1172.8 

49 

279.8 

8.67 

248.8 

924.4 

1173.2 

50 

281.0 

8.51 

250.1 

923.5 

1173.6 

52 

283.5 

8.20 

252.6 

921.7 

1174.3 

54 

285.9 

7.91 

255.1 

919.9 

1175.0 

56 

288.2 

7.65 

257.5 

918.2 

1175.7 

58 

290.5 

7.40 

259.8 

916.5 

1176.4 

HEAT 


85 


PRESSURE  TABLE  FOR  SATURATED  STEAM — (Continued.) 


Absolute 
pressure, 
Ib.  per  sq.  in. 

Temp., 
deg.  F. 

Sp.  vol.,      Heat  of 
cu.  ft.  per  Ib.   the  liquid 

Latent  heat 
of  evap. 

Total  heat 
of  steam 

P           t 

v  or  s 

h  or  q 

I  or  r 

h 

60 

292.7 

7.17        262.1 

914.9 

1177.0 

62 

294.9 

6.95        264.3 

913.3 

1177.6 

64 

297.0 

6.75        266.4 

911  .8 

1178.2 

66 

299.0 

6.56 

268.5 

910.2 

1178.8 

68 

301.0 

6.38 

270.6 

908.7 

1179.3 

70 

302.9 

6.20 

272.6 

907.2 

1179.8 

72 

304.8 

6.04 

274.5 

905.8 

1180.4 

74 

306.7 

5.89 

276.5 

904.4 

1180.9 

76 

308.5 

5.74 

278.3 

903.0 

1181.4 

78 

310.3 

5.60 

280.2 

901.7 

1181.8 

80 

312.0 

5.47 

282.0 

900.3 

1182.3 

82 

313.8 

5.34 

283  .  8 

899.0 

1182.8 

84 

315.4 

5.22 

285.5 

897.7 

1183.2 

86 

317.1 

5.10 

287.2 

896.4 

1183.6 

88 

318.7 

5  .  00 

288.9 

895.2 

1184.0 

90 

320.3 

4.89 

290.5 

893  .  9 

1184.4 

92 

321.8 

4.79 

292.1 

892.7 

1184.8 

94 

323.4 

4.69 

293  .  7 

891.5 

1185.2 

96 

324  .  9 

4.60 

295.3 

890.3 

1185.6 

98 

326.4 

4.51 

296.8 

889.2 

1186.0 

100 

327.8 

4.429 

298.3 

888.0 

1186.3 

105 

331.4 

4.230 

302.0 

885.2 

1187.2 

110 

334.8 

4.047 

305.5 

882.5 

1188.0 

115 

338.1 

3.880 

309.0 

879.8 

1188.8 

120 

341.3 

3.726 

312.3 

877.2 

1189.6 

125 

344.4 

3.583 

315.5 

874.7 

1190.3 

130 

347.4 

3.452 

318.6 

872.3 

1191.0 

135 

350.3 

3.331 

321.7 

869.9 

1191.6 

140 

353.1 

3.219 

324.6 

867.6 

1192.2 

145 

355.8 

3.112 

327.4 

865.4 

1192.8 

150 

358.5 

3.012 

330.2 

863.2 

1193.4 

160 

363.6 

2.834 

335.6       858.8 

1194.5 

170 

368.5 

2.675 

340.7 

854.7 

1195.4 

180 

373.1 

2.533 

345.6 

850.8 

1196.4 

190 

377.6 

2.406 

350.4 

846.9 

1197.3 

200 

381.9 

2.290 

354.9 

843.2 

1198.1 

225 

391.9 

2.046 

365.5 

834.4 

1199.9 

250 

401.1 

1.850 

375.2 

826.3 

1201.5 

300 

417.5 

1.551 

392.7 

811.3 

1204.1 

350 

431.9 

1.334 

408.2 

797.8 

1206.1 

400 

444.8 

1.17 

422.0 

786.0 

1208.0 

450 

456.5 

1.04 

435.0 

774.0 

1209.0 

500 

467.3 

0.93 

448.0 

762.0 

1210.0 

550 

477.3 

0.83 

459.0 

751.0 

1210.0 

600 

486.6 

0.76 

469.0 

741.0 

1210.0 

SECTION  III 
MINE  GASES 

GEOLOGICAL  CONDITIONS — COMMON  MINE  GASES — HYDRO- 
CARBON GASES — PROPERTIES  AND  BEHAVIOR  OF  MINE 
GASES — METHANE — FIREDAMP — CARBON  MONOXIDE — 
CARBON  DIOXIDE — BLACKDAMP — AFTERDAMP — INFLAM- 
MABLE AND  EXPLOSIVE  MINE  GASES. 

GEOLOGICAL  CONDITIONS 

Gas,  Oil  and  Water. — The  strata  of  the  earth's  crust  form 
a  great  natural  reservoir  for  gas,  oil  and  water.  These  collect 
in  the  formations,  in  the  order  of  their  relative  densities. 
As  illustrated  in  the  Fig.  11,  which  represents  an  ideal  geo- 


FIG.  11. 

logical  section,  the  subterraneous  water  collects  in  the  lower 
permeable  strata,  the  oil  next  above,  while  the  gas  is  found 
higher  on  the  anticline. 

This  condition  is  only  true,  however,  in  a  general  way, 
depending  on  the  nature  of  the  strata  and  their  power  to 
absorb  and  hold  these  elements.  Water,  and  oil  to  a  less 
extent,  find  their  way  by  gravity  to  a  " hard-pan"  or  stratum 
impervious  to  them;  while  gas  drains  to  the  surface  and 
escapes,  unless  confined  by  an  overlying  stratum  of  clay  or 
cil,  from  the  overlying  rocks  into  the  synclinal  basins,  creates 
enormous  pressures,  which  are  exerted  more  or  less  equally 
on  the  water,  oil  and  gas. 

86 


MINE  CASES  87 

Water  Level. — In  every  geological  section,  there  is  a  more 
or  less  defined  " water  level"  or  depth  at  which  water  is  found 
in  quantity.  Wells  or  boreholes  sunk  to  this  general  level 
strike  a  usually  abundant  supply  of  water.  The  same  is 
true,  but  to  a  less  extent,  of  oil,  in  oil  regions.  The  flow  of 
oil,  in  oil-bearing  rocks,  however,  is  not  as  free  as  that  of 
water,  owing  to  its  viscosity  and  limited  supply. 

The  water  level  is  not  constant,  but  varies  according  to 
the  changing  supply  or  surface  drainage,  being  higher  in 
wet  seasons  and  lower  in  seasons  of  drought.  As  the  oil 
floats  on  the  water  any  change  in  water  level  is  accompanied 
by  a  similar  change  in  the  oil  supply.  It  is  due  to  this  fact 
that  exhausted  oil  wells  often  become  productive  in  a  season 
of  flood,  and  producing  wells  frequently  cease  to  flow  in  a 
prolonged  season  of  drought. 

Natural  Gas. — All  gas  formed  and  contained  in  the  strata 
is  called  " natural  gas,"  in  distinction  from  gas  manufactured 
in  the  industries.  Natural  gas  commonly  occurs  in  large 
volume,  in  coal  formations,  where  it  accumulates  in  cavities 
or  pockets  and  in  crevices  in  the  strata.  It  is  very  largely  com- 
posed of  what  are  commonly  known  as  the  "hydrocarbon"  gases. 

Effect  of  Faults. — Fault  lines  and  other  geological  disturb- 
ances of  the  strata  have  opened  channels  by  which  the  gas 
confined  in  certain  strata  escape  to  other  strata  or  into  the 
mine  workings  or  to  the  surface.  For  this  reason,  the  near 
approach  of  the  working  face  to  a  fault  line  or  a  disturbed 
condition  of  the  strata  is  often  accompanied  by  a  marked 
change  in  the  gaseous  condition  of  the  mine  air.  The  percent- 
age of  gas  common  to  the  mine  may  then  either  increase  or 
decrease  depending  on  the  location  of  the  gas  and  the  nature 
of  the  fault. 

Gas  Feeders,  Blowers. — Any  continuous  flow  of  gas  from  a 
crack  or  crevice  in  the  strata  is  called  a  "gas  feeder,"  or 
simply  a  "feeder."  The  gas  flowing  from  the  crevice  is  known 
as  "feeder  gas." 

When  a  gas  feeder  is  under  high  pressure  so  that  the  gas 
issues  with  considerable  velocity,  the  feeder  is  called  a  "blower" 
and  the  gas  "  blower  gas." 


88  MINE  GASES  AND  VENTILATION 

Occluded  Gases. — The  gases  commonly  occluded  in  the  coal 
formations  .are  methane,  ethane,  nitrogen,  carbon  dioxide  and 
oxygen.  They  are  the  result  of  the  chemical  changes  that 
took  place  in  the  formation  of  the  coal;  or  are  produced  by 
the  action  of  acid  waters  on  certain  limestones  or  other  car- 
bonates. Occluded  gases  are  held  in  the  pores  of  the  coal 
and  other  strata,  from  which  they  drain  into  the  mine  open- 
ings, or  work  upward  through  such  pervious  strata  as  shale 
and  sandstone.  The  process  is  called  "emission"  or  "trans- 
piration" of  gases. 

Pressure  of  Occluded  Gas. — At  times,  the  gas  is  confined  in 
the  coal  or  other  strata  by  an  overlying  stratum  of  clay  or 
impervious  limerock  that  prevents  its  escape  to  the  surface, 
and  the  pressure  of  the  gas  is  then  often  very  great,  varying 
from  500  and  600  Ib.  per  sq.  in.  to  four  or  five  times  that 
amount.  This  pressure  is  manifested  in  different  ways.  As 
the  mine  workings  are  extended  the  flow  of  gas  into  the  mine 
increases  with  the  exposure  of  fresh  faces  of  coal,  except 
where  the  conditions  are  such  as  to  allow  the  gas  to  drain  off 
and  reach  the  surface. 

Effect  of  Gas  Pressure  in  Mining. — The  pressure  of  gas 
confined  in  the  coal  is  often  sufficient  to  splinter  the  coal  in 
its  effort  to  escape,  the  fine  coal  being  thrown  into  the  face 
of  the  miner  at  work.  At  times,  the  gas  escapes  from  the 
coal  with  a  peculiar  hissing  sound  known  as  the  "singing  of 
the  coal."  The  pressure  of  gas  in  the  roof  frequently  causes 
heavy  roof  falls,  and  gas  in  the  floor  causes  the  bottom  to 
heave.  In  some  instances,  the  gas  pressure  assists  the  ex- 
traction of  the  coal  and  lessens  the  work  of  the  miner  by 
helping  to  break  down  the  coal. 

Outbursts  of  Gas. — In  the  mining  of  gaseous  seams,  it  is 
not  uncommon  for  gas  to  work  in  the  strata  as  the  coal  is 
extracted.  As  a  result,  the  gas  often  accumulates  in  pockets 
as  shown  in  the  ideal  section,  Fig.  12.  The  settlement  of  the 
roof  incident  to  the  removal  of  the  coal  affords  opportunity 
for  the  gas  to  expand  and  work  forward  toward  the  opening. 
The  working  of  the  gas  in  the  strata  is  often  accompanied  by 
severe  "poundings"  or  "bumps,"  due  to  sudden  displacement 


MINE  CASES 


89 


of  the  gas.  Such  sounds  often  continue  for  several  days  pre- 
vious to  a  sudden  outburst  of  the  gas  into  the  mine  workings. 
The  continuance  of  these  poundings  are  a  sufficient  warning  to 
experienced  miners  to  vacate  that  part  of  the  mine  till  the 
strata  have  become 
more  quiet  by  the 
gradual  draining 
off  of  some  of  the 
gas. 

In  many  cases, 
where  the  gas 
works  down  into 
the  coal,  either  at 


7/^^ 


FlQ   12 


the  face  or  in  the 
"ribs,  "  as  shown 
in  the  figure  above, 

the  pressure  of  the  gas  becomes  distributed  over  a  considerable 
surface,  and  is  sufficiently  great  to  throw  down  the  coal. 
This  is  called  an  "  outburst"  of  gas,  since  large  volumes 
of  gas  escape  and  often  hundreds  of  tons  of  coal  are  thrown 
violently  into  the  opening. 

THE  COMMON  MINE  GASES 

The  gases  of  most  importance  in  coal  mining,  together  with 
their  chemical  symbols,  molecular  weights,  densities  referred 
to  hydrogen  and  specific  gravities  referred  to  air  of  the  same 
temperature  and  pressure,  are  the  following: 


Gas 

Symbol 

Molecular 
weight' 

Density 
H  =  1 

Spec.  gravity 
air  =  l 

Methane  (marsh  gas)  
Ethene  ,    Ethylene    (  olcfiant 

gas) 

CH4 
C2H4 

16 

28 

8 
14 

0.559 

0  978 

Ethane  
Carbon  monoxide  
Carbon  dioxide  .  .              ... 

C2H6 
CO 
CO2 

30 

28 
44 

15 
14 

22 

1  .  0366 
0.967 
1  529 

Hydrogen  sulphide 

H2S 

34 

17 

1   1912 

Oxygen  

O2 

32 

10 

1  .  1056 

Nitrogen   .... 

N2 

28 

14 

0  9713 

Hydrogen 

H2 

2 

1 

0  06936 

90 


MINE  GASES  AND  VENTILATION 


Occurrence  of  Mine  Gases. — Aside  from  the  oxygen  and 
nitrogen  of  the  air,  the  gases  commonly  occurring  in  coal 
mines  are  methane,  carbon  dioxide,  carbon,  monoxide,  and 
less  frequently  or  in  less  quantity,  hydrogen  sulphide  and 
olefiant  gas.  These  gases  are  produced  by  the  processes  of 
decomposition  or  combustion  constantly  going  on  in  the  mine, 
or  they  emanate  from  the  coal  or  other  strata,  where  they 
exist  as  natural  gases. 

Condition  of  Gas  Confined  in  Coal. — The  results  of  careful 
experimental  study  of  coal  indicate  (Chamberlin)  that  gas 
may  exist  in  coal  in  three  different  ways:  1.  The  gas  is  oc- 
cluded, in  a  true  sense,  or  absorbed  (possibly  condensed)  by 
the  coal.  2.  The  gas  is  entrapped  or  held  mechanically  in 
the  cavities,  cracks  or  pores  of  the  coal.  3.  The  gas  may 
result  from  chemical  changes  going  on  in  the  coal. 

Escape  of  Gas  from  Coal. — Experiments  made  by  the  Bu- 
reau of  Mines,  by  crushing  weighed  samples  of  different  coals 
in  closed  vessels  of  known  capacity,  show  that  coal  con- 
tinues to  give  Off  gas  for  a  long  time  after  it  is  mined. 

Coal  exposed  to  the  atmosphere  loses  much  of  its  occluded 
gas,  but  the  gas  is  liberated  more  freely  by  crushing  the  coal, 
which  would  indicate  that  much  of  the  gas  is  held  mechan- 
ically within  the  mass.  It  is  also  shown  that  the  coal  con- 
tinues to  absorb  oxygen  from  the  air,  during  the  same  period. 

The  following  table  gives  the  percentages,  by  volume,  of  the 
constituents  of  natural  gases  obtained  from  various  coals,  in 
different  localities. 

TABLE  SHOWING  THE  COMPOSITION  OF  GAS  EVOLVED  FROM  COALS  AT 
212  DEG.  F.,  IN  VACUO 


Locality 

CH4 

N2 

C02 

0-2 

.C2H6 

Remarks 

South  Wales  
South  Wales  
South  Wales 

63.76 
87  30 

62.78 
29.75 
7.33 

36.42 
5.44 
5.04 

0.80 
1.05 
0.33 

.... 

Bituminous 
Bituminous 
Steam  coal 

South  Wales  

93.13 

4.25 

2.62 

Anthracite 

Lancashire  
Lancashire  

80.69 
77.19 

8.12 
5.96 

6.44 
9.05 

4.75 
7.80 

Cannel 
Cannel 

Westphalia 

89  91 

7.50 

2.59 

Gas  coal 

Westphalia 

34  85 

58  48 

2.56 

4.11 

Gas  coal 

MINE  GASES 


91 


Composition  of  Feeder  or  Blower  Gas. — A  large  number  of 
analyses  of  gas  issuing  from  coal  seams  as  "feeders"  or 
"blowers"  have  been  made.  Gas  has  also  been  obtained  by 
drilling  holes  several  feet  into  the  face  of  the  coal.  These 
analyses  show  a  wide  variation  in  the  composition  of  the 
gas  in  different  localities.  Moreover,  since  the  rate  of  emis- 
sion of  gases  varies,  the  composition  of  feeder  gas  is  only 
suggestive  of  the  contamination  of  the  mine  air. 

The  following  table  gives  the  composition,  by  volume,  of 
blower  gas  in  different  localities,  which  shows  in  a  general 
way  a  higher  percentage  of  methane,  in  comparison  with  that 
of  nitrogen.  This  may  be  due,  to  a  large  extent,  to  the 
higher  rate  of  transpiration  of  the  methane,  as  compared 
with  nitrogen,  which  tends  to  increase  its  percentage  in  blower 
gas  over  what  actually  exists  in  the  pores  of  the  coal : 

TABLE  GIVING  COMPOSITION  OF  BLOWER  GAS  IN  DIFFERENT  LOCALITIES 


Locality 

CH4 

N, 

C02 

O2 

CO 

C2H4 

Austria            

88  9 

10  8 

1  0 

0  3 

Austria 

99  1 

0  7 

0  2 

Austria  

90  0 

9  2 

0  2 

0  6 

Germany             

87  2 

11  7 

1  l 

Germany 

77  7 

18  5 

3  7 

0  1 

South  Wales  

96  7 

2  8 

0  5 

Wallsend,  England 

92  8 

6  9 

0  3 

Jarrow,  England  
Oakwellgate,  England  

83.1 

98  2 

14.2 
1  3 

2.1 
0  5 

0.6 

Wilkes-Barre,  Penn  

94.2 

3:3 

1.1 

0.9 

0.1 

0.4 

It  is  important  to  remember  that  the  occluded  gases  of 
coal  are  not  chemically  combined  with  the  constituents  of 
the  coal  as  shown  by  analysis,  and  do  not  form  a  part  of  the 
coal  itself,  although  adding  much  to  its  inflammability  and 
heat  value. 

HYDROCARBON  GASES 

General  Formulas  of  Hydrocarbon  Gases. — Carbon  (C)  and 
hydrogen  (H)  unite  in  different  ways  to  form  groups  of  com- 
pounds, having  certain  distinct  characteristics.  Such  are 


92  MINE  GASES  AND  VENTILATION 

the  " paraffins,"  represented  by  the  general  f  ormula  CnH2n+2; 
the  "defines,"  CnH2n;  the  "acetylenes,"  CnH2n_2;  and 
other  compounds  of  less  importance  in  mining,  as  the  "  ben- 
zenes," "naphthalines,"  etc. 

Occurrence  and  Formation. — Methane  or  light  carbureted 
hydrogen  (CH4)  and  ethane  (C2H6),  belong  to  the  paraffin 
or  fatty  group,  while  olefiant  gas  (C2H4)  belongs  to  the  olefine 
or  oily  group.  These  are  all  products  of  the  destructive  distil- 
lation of  organic  matter.  Methane  is  often  seen  bubbling  up 
from  the  bottom  of  stagnant  pools,  in  marshes,  which  fact 
suggested  the  name  "marsh  gas."  It  is  the  result  of  the  slow 
decay  of  the  vegetable  matter  (in  the  presence  of  water  and 
absence  of  air),  at  the  bottom  of  the  pool. 

On  the  other  hand,  olefiant  gas  is  the  result  of  the  dry 
distillation  of  gas  from  organic  matter,  which  takes  place 
less  frequently  in  the  strata,  owing  to  the  almost  invariable 
presence  of  moisture.  The  character  of  these  hydrocarbon 
gases,  moreover,  varies,  also,  with  the  kind  of  organic  matter 
that  undergoes  decomposition. 

Of  the  hydrocarbon  gases,  the  paraffins  (methane  and 
ethane)  are  the  ones  chiefly  occluded  in  the  coal  measures; 
while  olefiant  gas,  belonging  to  the  olefine  group  is  rarely 
found  even  in  minute  quantity.  Beside  the  hydrocarbon  gases 
occluded  in  coal,  as  has  been  stated,  varying  quantities  of 
nitrogen,  oxygen  and  carbon  dioxide  have  been  absorbed. 

The  Heavy  Hydrocarbon  Gases.— The  heavy  hydrocarbons 
occur  in  the  coal  measures  as  occluded  gases,  only  to  a  limited 
extent.  Of  these,  there  are  but  two  that  are  worthy  of 
mention;  they  are 

Olefiant  gas,  ethene  or  ethylene,  (C2H4);  sp.  gr.,  0.978; 

Ethane,  (C2H6);  sp.  gr.,  1.0366. 

Both  of  these  gases  are  colorless  and  odorless;  they  occur 
but  to  a  limited  extent  in  association  with  methane ;  and  their 
chief  importance  lies  in  the  fact  that  they  each  have  a  wider 
explosive  range  and  a  lower  temperature  of  ignition  than  pure 
methane.  The  analyses  of  the  gases  exuded  from  coal  rarely 
show  any  appreciable  quantity  of  olefiant  gas  (ethene);  but 
ethane  (C2H6)  occurs  more  frequently  as  an  occluded  gas. 


MINE  GASES  93 

PROPERTIES  AND  BEHAVIOR  OF  MINE  GASES 

The  symbols,  molecular  weights,  densities  and  specific 
gravities  of  the  common  mine  gases  have  been  given  in  an- 
other place.  The  properties  and  behavior  of  these  gases  in 
the  mine  will  be  treated  here  from  a  practical,  rather  than  a 
theoretical  standpoint. 

METHANE 

This  gas  is  commonly  known  as  " marsh  gas"  or  " light 
carbureted  hydrogen,"  it  being  the  lightest  of  the  hydro- 
carbon gases.  It  is  a  colorless,  odorless  and  tasteless  gas.  It 
is  combustible,  burning  with  a  pale-blue  flame,  in  the  air  or 
in  oxygen.  It  contains  no  oxygen  and  is  not,  therefore,  a 
supporter  of  combustion,  in  the  generally  accepted  meaning 
of  the  term.  A  lamp  flame  is  quickly  extinguished  by  this 
gas  unmixed  with  air.  Mixed  with  air  in  certain  proportions, 
the  gas  becomes  explosive,  the  mixture  being  known  as  "  fire- 
damp. "  Marsh  gas  is  not  poisonous,  but  when  unmixed  with 
air  suffocates  by  excluding  oxygen  from  the  lungs.  The  di- 
luted gas  can  be  breathed  for  a  long  time  with  no  ill  effects, 
except  a  slight  dizziness,  which  quickly  passes  away  on  re- 
turn to  fresh  air. 

Marsh  gas  is  the  most  common  of  the  occluded  gases  of 
the  coal  formations.  It  seldom,  if  ever,  occurs  pure,  but  is 
mixed  in  varying  proportions  with  other  hydrocarbons  (olefi-" 
ant  gas  and  ethane)  and  often  with  nitrogen.  These  mixed 
gases  greatly  modify  the  character  and  properties  of  the  pure 
gas. 

Marsh  gas  issues  from  the  strata  into  the  mine  workings 
where  it  accumulates  in  quantity,  unless  removed  by  a  copious 
air  current.  The  most  gaseous  seams  are  those  that  are  over- 
laid with  a  compact  rock,  slate,  or  shale  that  is  impervious  to 
gas  and  not  traversed  by  faults,  which  would  allow  the  gas 
to  escape.  Gas  is  generated  most  freely  from  a  virgin  seam 
and  from  a  freshly  exposed  face  of  coal.  Hence,  new  work- 
ings generate  more  gas  than  old  workings;  because,  in  the 
old  workings,  the  gas  has  mostly  drained  from  the  strata  and 
escaped. 


94  MINE  GASES  AND  VENTILATION 

Marsh  gas  diffuses  rapidly  into  the  air  and  other  gases, 
the  rate  of  diffusion  depending  on  the  relative  densities  of 
the  two  mediums.  The  question  is  often  asked,  if  the  diffu- 
sion of  gas  is  so  rapid  how  is  it  possible  for  a  large  body  of  gas 
to  accumulate  in  a  void  place  in  the  mine.  The  reason  is 
that  diffusion  only  takes  place  at  the  surface  of  contact,  and 
is  therefore  limited,  and  the  gas  is  being  generated  faster 
than  it  passes  away. 

Marsh  gas  being  lighter  than  air  tends  to  accumulate  at 
the  roof  and  at  the  head  of  steep  pitches  and  in  rise  workings. 
It  is  found  in  such  places  where  the  air  current  is  not  suffi- 
ciently strong  to  sweep  away  the  gas  and  in  other  poorly 
ventilated  or  abandoned  places.  Gas  can  generally  be  found 
at  the  roof  or  .close  to  the  face  of  the  coal  in  chambers  gen- 
erating gas.  It  is  detected  by  observing  the  flame  of  a  safety 
lamp.  If  gas  is  present  in  sufficient  quantity  in  the  air  a 
faint  non luminous  cap  will  appear  surmounting  the  flame  of 
the  lamp.  The  gas  also  lengthens  and  enlarges  the  flame. 

FIREDAMP 

All  gases  were  formerly  known  to  the  miner  as  "damps," 
which  is  a  word  of  Dutch  or  German  origin  meaning  vapor  or 
fumes..  Later,  as  the  characters  of  the  different  gases  became 
known,  they  were  named  according  to  their  several  charac- 
teristics. The  term  " firedamp"  was  applied  to  any  inflam- 
mable or  explosive  mixture  of  gas  and  air. 

The  word  firedamp,  today,  in  this  country,  means  any  in- 
flammable or  explosive  mixture  of  marsh  gas  and  air,  with 
or  without  other  gases.  In  England,  the  word  is  taken. to 
mean  any  mixture  of  marsh  gas  and  air  without  regard  to 
whether  or  not  the  mixture  was  inflammable  or  explosive, 
which,  however,  is  not  its  logical  meaning. 

When  but  a  small  amount  of  marsh  gas  is  mixed  with 
pure  air  the  gas  is  so  diluted  that  the  mixture  is  not  inflam- 
mable. In  contact  with  flame,  this  small  percentage  of  gas 
in  the  air  adds  to  the  combustion  and  lengthens  and  enlarges 
the  flame;  but  the  flame  is  not  propagated  throughout  the 


MINE  GASES  95 

mixture,  as  the  absorption  of  the  heat  by  the  air  is  too  great 
to  maintain  the  temperature  necessary  for  combustion. 

Lower  Inflammable  Limit. — As  more  gas  is  added  to  the  air, 
a  point  is  soon  reached  where  the  combustion  of  the  gas  de- 
velops sufficient  heat  to  raise  the  temperature  of  the  air  to 
that  required  to  maintain  the  combustion.  When  this  point 
is  reached  the  flame  causing  the  ignition  is  extended  or  propa- 
gated through  the  mixture.  In  other  words,  the  mixture 
becomes  inflammable,  because  the  combustion  is  supported  in 
the  mixture  independent  of  any  other  source.  The  theoretical 
percentage  of  gas  in  the  firedamp  at  this  point,  as  calculated, 
is  slightly  above  2  per  cent.,  for  dry  air  or  saturated  air. 
The  heat  absorbed  by  the  water  of  saturation  is  so  slight  in 
comparison  that  it  can  be  ignored  without  appreciable  error. 
There  are  heat  losses,  however,  that  cannot  be  calculated, 
which  fact  raises  the  lower  inflammable  limit  of  pure  marsh 
gas  to  between  4  and  5  per  cent. 

Effect  of  Dust  and  Other  Gases. — Owing  to  the  fact  that 
marsh  gas  is  rarely,  if  ever,  found  pure,  but  is  generally 
mixed  with  dust  or  other  gases  or  both,  it  is  never  safe  to  work 
with  open  lights,  in  air  containing  more  than  1  per  cent, 
of  gas,  in  bituminous  mines;  or  2J^  per  cent,  in  anthracite 
mines. 

Gases  are  divided  into  two  general  classes,  in  respect  to 
the  effect  they  produce  on  the  inflammability  of  firedamp. 
Gases  having  a  lower  ignition  point  than  marsh  gas,  as  for 
example,  carbon  monoxide,  hydrogen  sulphide,  ethane  and 
olefiant  gas,  lower  the  inflammable  limit  of  firedamp,  as  given 
above.  Fine  coal  dust  floating  in  the  mine  air  has  a  similar 
effect,  in  proportion  as  the  dust  is  highly  inflammable.  On 
the  other  hand,  extinctive  gases  such  as  nitrogen  and  carbon 
dioxide  raise  the  limit  given  above. 

In  the  working  of  bituminous  mines,  coal  dust  is  a  most 
dangerous  factor,  especially  when  the  coal  is  highly  inflam- 
mable. In  many  cases,  the  finely  divided  dust  produces  an 
explosive  atmosphere  even  when  no  gas  is  present.  The  pres- 
ence of  such  dust  in  the  mine  air,  acted  on  by  the  flame  of  a 
blownout  shot,  is  certain  to  cause  trouble. 


96  MINE  CASES  AND  VENTILATION 

To  Calculate  the  Lower  Inflammable  Limit. — In  order  to 
calculate  the  proportion  of  gas  (methane)  and  air  when  the 
firedamp  mixture  first  becomes  inflammable,  it  must  be  as- 
sumed that  all  the  heat  generated  by  the  combustion  of  the 
gas  is  absorbed  by  the  products  of  the  combustion  and  thi? 
remaining  unburned  air.  Owing,  however,  to  there  being  a 
certain  amount  of  heat  lost  by  radiation  or  otherwise  that 
cannot  be  estimated  or  accounted  for,  the  calculated  inflam- 
mable limit  will  only  approach  the  actual,  to  the  extent  that 
the  conditions  are  fully  realized  in  the  calculation.  The  proc- 
ess is  as  follows: 

The  weight  of  oxygen  necessary  to  burn  1  Ib.  of  methane  or 
marsh  gas  (CH4)  is  shown  by  the  relative  weights  of  these 
gases  in  the  following  reaction : 

CH4  +  2O2  =  CO2  +  2H2O 

Molecular  weights 16  64         44  36 

Relative  weights 1  4  2%         2>£ 

But  oxygen  forms  23  per  cent.,  by  weight,  of  the  air,  the 
remaining  77  per  cent,  being  practically  all  nitrogen.  The 
weight  of  nitrogen  concerned  in  burning  1  Ib.  of  this  gas  in 
air  is  then  calculated  as  follows : 

23  :  77  ::4  :  N 
and  N  =  ^^  =  13.39  Ib. 

£i€t 

The  table  giving  the  heats  of  combustion  of  different  sub- 
stances (p.  66)  shows  that  methane,  burned  in  air  or  oxygen, 
gives  out  23,513  heat  units  (B.t.u.).  The  temperature  of  igni- 
tion of  this  gas  is  1200°  F. 

Now,  since  the  specific  heat  of  a  substance  is  the  heat 
(B.t.u.)  absorbed  by  1  Ib.  of  that  substance,  during  a  rise  of 
1  deg.  F.  in  its  temperature,  the  heat  absorbed  by  the  prod- 
ucts of  combustion  of  1  Ib.  methane,  for  each  degree  rise  in 
temperature,  is  found  by  multiplying  the  specific  heat  of  each 
of  the  products,  including  the  nitrogen  of  the  air,  by  the  rela- 
tive weight  of  each  product,  respectively.  The  total  heat  is 
then  found  by  multiplying  that  result  by  the  number  of  de- 


MINE  GASES  97 

grees  rise  in  temperature;  and  adding  the  latent  heat  in  the 
steam  or  water  vapor,  as  follows: 

The  specific  heats  of  the  several  products  of  combustion, 
referred  to  water  as  unity  (1),  are  carbon  dioxide,  0.2163; 
nitrogen,  0.2438;  water  vapor,  0.4805;  and  air,  0.2374.  The 
latent  heat  of  the  water  vapor  (steam)  or  the  heat  absorbed 
when  1  Ib.  ,water  becomes  steam  at  212°F.  is  970.4  B.t.u.  The 
heat  absorbed  by  the  products  of  combustion,  for  a  rise  of 
1200  -  32  =  1168°F.,  is  therefore 

Carbon  dioxide,    0.2163  X    2.75X1168=    694.7264 

Nitrogen,  0.2438  X  13.39  X  1168=  3812.9360  4507.6624  B.t.u. 


Water,  1.0000  X    2.25  X    180=    405.0000 

Latent  heal,      970.4000  X    2.25  =2183.4000 

Water  vapor,        0.4805  X    2.25  X  988  =  1068.1515  3656.5515  B.t.u. 


Total  heat  absorbed  by  products  ..............  8164.2139  B.t.u. 

Having  found  the  heat  absorbed  by  the  products,  the  next 
step  is  to  find  the  heat  absorbed  by  the  unburned  air.  Let  x  = 
weight  of  air  required  to  make  1  Ib.  of  the  gas  inflammable; 
and,  since  1  Ib.  CH4  consumes  4  Ib.  O  +  13.39  Ib.  N  =  17.39  Ib. 
air,  the  unburned  air  is  x  —  17.39  Ib.  The  original  tempera- 
ture of  the  air  being  60°F.,  the  rise  is  1200  -  60  =  1140  deg. 
and  the  heat  absorbed  is  0.2374(z  -  17.39)1140  -  270.636z 
-  4706.36  B.t.u.,  which  makes  the  total  heat  absorbed 

8164.2139+270.636z-4706.36  =  270.636z+3457.8539£.£.w. 

Since  the  heat  absorbed  is  assumed  equal  to  the  heat  gen- 
erated, 

270.636z  +  3457.8539  =  23,513  B.t.u. 
23,513  -  3457.8539       _  .     „  „       . 


alld 


270636 


This  is  the  total  weight  of  air  required  to  make  1  Ib.  of 
methane  (CH4)  inflammable.  In  other  words,  the  weight 
ratio  of  gas  to  air,  at  the  lower  inflammable  limit,  is  1  :  74.10. 
But  since  the  specific  gravity  of  methane,  referred  to  air  as 
unity,  is  0.559,  the  volume  ratio  of  gas  to  air,  at  this  point,  is 
1  :  0.559  X  74.10;  or  1  :  41.42.  That  is  to  say,  a  mixture  of 

7 


98  MINE  GASES  AND  VENTILATION 

pure  methane  and  air  first  becomes  inflammable  when  1  vol- 
ume of  this  gas  is  mixed  with  41.42  volumes  of  air. 
The  percentage  of  gas  in  this  mixture  is 

fTlL42  X  10°  "  4^f2  =  2'3  Per  CmL 

Lower  Explosive  Limit. — The  continued  addition  of  gas  to 
the  air  causes  the  firedamp  mixture  to  become  more  and 
more  inflammable  till  a  point  is  reached  when  the  combustion 
of  the  gas  is  so  rapid  that  the  mixture  is  explosive.  As  this 
condition  is  approached,  in  practice,  owing  to  the  mixture  of 
the  gas  and  air  not  being  uniform,  the  ignited  gas  often  snaps 
and  cracks  in  the  combustion  chamber  of  a  safety  lamp. 

In  the  same  manner,  an  accumulation  of  firedamp,  in  the 
mine,  when  ignited,  may  burn  with  greater  or  less  energy  or 
violence  and  small  explosions  may  occur  here  and  there,  fol- 
lowed perhaps  by  the  general  explosion  of  the  entire  body  of 
the  firedamp.  The  explosion  depends  not  alone  on  the  propor- 
tion of  gas  and  air  in  the  mixture,  although  that  is  important, 
but  on  the  intensity  and  volume  of  the  igniting  flame.  Thus, 
it  happens  that  a  firedamp  mixture  ignited  in  the  narrow 
confines  of  the  mine  workings  may,  after  burning  for  a  brief 
period  with  more  or  less  energy,  suddenly  develop  a  violent 
explosion. 

The  lower  explosive  limit  of  pure  methane  has  been  de- 
termined, by  experiment,  to  occur  when  1  volume  of  the  gas 
is  mixed  with  13  volumes  of  air;  or  the  percentage  of  gas  in 
the  mixture  is 


X  100  =  -^  =  7-14  P^  cent. 

This  limit,  however,  is  considerably  modified  by  any  condi- 
tions that  tend  to  increase  or  decrease  the  amount  of  heat 
developed. 

Maximum  Explosive  Point. — The  maximum  explosive  force 
of  a  combustible  gas  is  developed  when  the  proportion  of  gas 
to  air  is  just  sufficient  for  complete  combustion.  If  the  gas  in 
the  mixture  is  in  excess  of  this  proportion  the  full  heat  en- 
ergy is  not  developed,  owing  to  the  incomplete  combustion  of 


MINE  GASES  99 

the  gas.  On  the  other  hand,  if  the  air  is  in  excess  of  what 
is  required  for  complete  combustion,  the  unburned  air  ab- 
sorbs a  portion  of  the  heat  generated  by  the  combustion, 
which  thus  becomes  latent. 

The  maximum  explosive  force  of  methane  is  developed 
when  the  proportion  of  gas  to  air  is  1  :  9.57.  -  It  is  calculated 
in  the  following  manner:  Write,  again,  the  chemical  equation 
expressing  the  reaction  that  takes  place  when  this  gas  burns 
in  oxygen,  forming  carbon  dioxide  and  water;  thus, 

CH4  +  2O2  =  CO2  +  2H2O 
Molecular  volumes,        1212 

It  should  be  observed  that  when  the  symbol  of  each  gas 
is  written  as  a  molecule  (oxygen  =  O2)  the  prefix  or  number 
written  before  the  symbol,  indicating  the  number  of  mole- 
cules of  that  gas  taken,  shows  also  the  relative  volume  of  the 
gas  concerned  in  the  reaction;  because  the  volume  of  all 
gaseous  molecules  at  the  same  temperature  and  pressure  is 
the  same. 

The  above  equation  shows  that  two  volumes  of  oxygen 
(2O2)  are  required  to  completely  burn  one  volume  of  methane 
(CH4);  and  there  are  formed  one  volume  of  carbon  dioxide 
(CO2)  and  two  volumes  of  water  (2H2O). 

But,  oxygen  forms  20.9  per  cent.,  by  volume,  of  the  at- 
mosphere. Therefore,  when  methane  is  burned  in  air,  the 
volume  of  air  required  to  completely  burn  two  volumes  of  the 
gas  is 

2  volumes 

~0209~  =  9>569'  Say  9'57  voL 

Hence  the  proportion  of  gas  to  air  that  will  develop,  in  ex- 
plosion, the  maximum  force  is  1  :  9.57.  The  percentage  of 
gas  in  the  mixture,  at  this  point,  is 


Higher  Explosive  Limit.  —  The  continued  addition  of  gas 
after  the  maximum  explosive  point  is  reached,  causes  the  ex- 
plosion of  the  firedamp  mixture  to  be  less  and  less  violent, 
till  a  point  is  finally  reached  where  the  proportion  of  air  is  so 


100  MINE  GASES  AND  VENTILATION 

* 

reduced    that    explosion    ceases    and    the    mixture    becomes 
simply  inflammable. 

The  point  at  which  explosion  ceases  is  called  the  "  higher 
explosive  limit,"  For  pure  methane,  this  point  is  practically 
reached  when  the  proportion  of  gas  to  air  is  1  :  5,  although  the 
position  and  character  of  the  igniting  flame,  may  vary  this  pro- 
portion slightly.  The  percentage  of  gas  in  the  firedamp,  at 
this  point,  is  practically 

;  X  100  =  ~  =  16.67  per  cent. 

1    -)-  5  D 

Higher  Inflammable  Limit. — By  the  continued  addition  of 
gas,  the  firedamp  having  ceased  to  be  explosive,  now  becomes 
less  and  less  inflammable.  The  mixture  not  only  ignites  less 
readily,  but  when  ignited  burns  less  regularly  and  quietly  than 
did  the  same  firedamp  mixture,  in  the  lower  inflammable  stage 
when  less  gas  and  more  air  were  present. 

The  higher  inflammable  stage  of  the  gas  is  more  danger- 
ous, in  mining  practice,  than  the  lower  inflammable  stage  of 
the  same  gas,  because  the  slightest  addition  of  air,  which  is 
liable  to  occur  at  any  moment  in  the  mine,  causes  the  mix- 
ture to  approach  the  maximum  explosive  point.  The  addi- 
tion of  air  to  firedamp  in  the  lower  explosive  or  inflammable 
stages  makes  the  mixture  less  explosive  or  inflammable. 

Another  important  distinction  between  the  lower  and 
higher  stages  of  firedamp  mixtures  is  the  relative  ease  with 
which  the  flame  cap  may  be  detected  in  the  two  stages.  While 
the  flame  of  a  safety  lamp  burns  steadily  and  yields  a  good 
cap  that  is  easily  detected,  in  the  lower  inflammable  stage; 
the  lamp  flame  is  unsteady  and  the  flame  cap  generally  hard 
to  discern  in  the  higher  inflammable  stage.  The  reason  is 
probably  to  be  found  in  the  uncertain  and  varying  amount 
of  air  in  the  mixture  feeding  the  flame,  which  makes  the  gas 
continually  approach  the  explosive  point  The  gas  in  this 
(higher)  stage  is  said  to  be  "  sharp." 

The  following  table  will  make  the  several  stages  of  fire- 
damp more  clear;  but  it  must  be  remembered  the  proportions 
of  gas  to  air  and  percentages  of  gas  given  as  marking  the 


MINE  GASES 


101 


dividing  line  between  the  different  stages  or  the  inflammable 
and  explosive  limits  are  only  suggestive  and  vary  with  the 
degree  of  purity  of  the  gas;  the  volume,  intensity  and  posi- 
tion of  the  igniting  flame,  and  the  pressure  and  temperature 
of  the  surrounding  atmosphere. 

FIREDAMP  MIXTURES  (METHANE  AND  AIR) 


Lower 

Explosive 

stages                                              Higher 

inflammable 



— 

inflammable 

stage 

Lower  stage 

Maximum 

point                 Higher  stage 

stage 

Proportion  of  Gas  to  Air 


1  :40 

|      1  :13 

1:9.  57 

1  :5 

1  :2.4 

2.5% 

7.14% 

I 

Percentage  of  Gas 

9.46% 

16.67% 

29.5% 

The  continued  addition  of  gas  thus  renders  the  firedamp 
extinctive  of  its  own  flame  and  therefore  noninflammable. 
The  proportions  and  percentages  given  in  the  table  denote 
more  or  less  closely  the  limits  of  the  several  stages. 

Flashdamp. — -This  is  a  mixture  composed  almost  wholly  of 
marsh  gas  (CH4)  and  carbon  dioxide  (CO2),  mixed  in  the  pro- 
portion in  which  these  gases  diffuse  into  each.  It  is  formed 
under  special  conditions,  in  mines,  where  carbon  dioxide  from 
the  old  workings  of  an  abandoned  seam  becomes  mixed  with 
the  undiluted  marsh  gas  generated  in  the  strata.  The  mix- 
ture is  lighter  than  air  and  possesses  the  peculiar  and  mis- 
leading property  of  extinguishing  the  lamp  at  the  roof  of 
the  .seam  or  the  face  of  a  steep  pitch. 

Calculation  of  Composition  of  Flashdamp. — According  to 
the  law  of  diffusion,  gases  diffuse  into  each  other  in  the  in- 
verse ratio  of  the  square  roots  of  their  densities  or  specific 
gravities.  For  example,  the  specific  gravities  of  methane 
and  carbon  dioxide  are  0.559  and  1.529,  respectively;  and  the 
ratio  of  the  velocities  of  diffusion  of  these  two  gases  into 
each  other  is  then  the  inverse  ratio  of  the  square  roots  of 
these  numbers. 

CH4  =   VL529       L236  = 
C02  ~  0.747  = 


102  MINE  GASES  AND  VENTILATION 

which  can'  be  written  1.65  :  1  ;  or  1650  :  1000.  This  ratio 
shows  that  when  these  gases  diffuse'  into  each  other,  directly, 
before  dilution  with  air  takes  place,  the  mixture  will  contain 
1650  volumes  of  methane  for  each  1000  volumes  of  carbon  di- 
oxide. The  same  result  is  obtained  by  stating  the  law  thus: 
The  ratio  of  diffusion  is  equal  to  the  square  root  of  the  inverse 
ratio  of  the  densities  or  specific  gravities  of  the  gases;  or,  as 
follows: 

CH4          /1.  529          / 

CO,  ==V0559  =:  V  2.735: 

A  slightly  different,  though  theoretically  more  correct  re- 
sult is  obtained  when  the  calculation  is  based  on  the   den- 
sities of  these  gases,  referred  to  hydrogen  as  unity  (1).     The 
process  is  as  follows: 
Methane  (CH4)  : 

Q    =  1  X  12  =  12 
H4  =  4  X     1  =      4 

Molecular  wt.  ==16;    density,  16  -r-  2  =  8 
Carbon  dioxide  (CO2)  : 

C    =  1  X  12  =  12 
02  =  2  X  16  =  32 

Molecular    wt.  =  44;    density,  44  -f-  2  =  22 
The  ratio  of  diffusion  is  then  equal  to  the  square  root  of 
the  inverse  ratio  of  these  densities;  or 


~*  =  Jf  =  V2J5  =  1.658 

^U2  \    O 


Calculation  of  Percentage  Composition,  by  Volume.  —  The 
mixture  is  estimated  to  contain 

Methane  (CH4)  .................  ..............  ____  1658  volumes; 

Carbon  dioxide  (CO2)  .........................  ....  1000  volumes; 

Total  .  .  ........................................  2658  volumes. 

Percentage,  by  volume, 

Methane,  165^Q100  =  62.38  per  cent. 


1000  X  100 
Carbon  dioxide,  -^r^  --   =  37.62  per  cent. 


100.00  per  cent. 


MINE  GASES  103 

CARBON  MONOXIDE 

This  gas,  formerly  known  in  mining  textbooks  as  "car- 
bonic oxide/'  or  "whitedamp,"  is  the  product  of  the  com- 
bustion of  carbon  in  a  limited  supply  of  pure  air.  Because 
the  supply  of  oxygen  is  limited  the  combustion  of  the  carbon 
is  incomplete  and  the  monoxide  is  formed  instead  of  the 
dioxide. 

Carbon  monoxide  is  a  colorless  gas.  It  is  extremely 
poisonous,  owing  to  its  being  absorbed  very  rapidly  by  the 
haemoglobin  or  red  coloring  matter  of  the  blood,  from  which 
it  is  separated  slowly  and  with  difficulty.  The  effect  on  the 
system  is  therefore  cumulative  when  exposed  to  the  smallest 
percentage  of  this  gas  in  the  atmosphere  breathed.  The 
affinity  of  carbon  monoxide  for  the  haemoglobin  is  from  250 
to  400  times  as  great  as  that  of  oxygen,  so  that  the  blood 
corpuscles  are  quickly  rendered  inert  and  death  is  the  sure 
result.  The  gas  is  not  displaced  by  the  oxygen  administered  in 
treatment,  but  is  eliminated  slowly  by  natural  processes  that 
take  place  in  the  system,  unless  the  latter  is  too  weak  or  the 
percentage  of  the  gas  absorbed  is  too  great  for  such  result 
to  take  place. 

The  treatment  for  carbon-monoxide  poisoning  is  the  en- 
forced inhalation  of  pure  oxyge'n,  by  the  use  of  the  pulmotor. 
This  is  a  device  that  consists  essentially  of  a  small  portable 
tank  containing  compressed  oxygen,  which  is  pumped  into 
the  lungs  by  a  bellows,  while  another  belows  withdraws 
the  same  from  the  lungs  after  use.  The  pressure  of  the  gas 
in  the  oxygen  tank  automatically  operates  the  bellows  at 
a  rate  of  16  strokes  per  minute  as  in  normal  breathing.  A 
face  mask  completes  the  equipment.  It  is  important  to  draw 
the  tongue  forward  with  tongs  provided  for  that  purpose, 
and  to  close  the  gullet  leading  to  the  stomach,  by  a  gentle 
pressure  of  the  thumb  on  the  throat,  in  order  to  avoid  the 
gas  filling  the  stomach. 

The  presence  of  the  smallest  percentage  of  carbon  mon- 
oxide in  the  atmosphere  breathed  is  dangerous  to  health  and 
life  because  of  its  cumulative  tendency,  its  possible  toxic 
effect  on  the  nervous  system  and  the  impairment  of  the  vital 


104  MINE  GASES  AND  VENTILATION 

organs  of  the  body.  The  fatal  percentage  of  this  gas  cannot 
be  definitely  stated  because  of  numerous  other  factors  that 
together  determine  a  fatal  effect.  The  more  important  of 
these  are  the  following:  The  depletion  of  the  oxygen  of  the 
air  breathed;  the  length  of  the  time  of  exposure  to  the  poi- 
sonous atmosphere;  the  energy  expended  in  physical  work 
in  such  atmosphere ;  the  state  of  health  and  the  normal  physical 
condition  of  the  person. 

Some  persons  are  more  sensitive  to  gas  poisoning  than 
others,  owing  to  a  less  vigorous  constitution,  a  temporarily 
weakened  condition,  a  more  nervous  temperament,  or  pre- 
vious exposure  to  gas  poisoning,  the  baneful  effects  being  hard 
to  eradicate  from  the  system.  For  these  reasons,  what  would 
prove  a  fatal  percentage  in  some  instances  of  less  purity  of 
atmosphere,  longer  exposure,  more  difficult  work,  or  physical 
ailment  of  any  nature,  would  not  necessarily  produce  fatal 
results  under  better  conditions  and  more  robust  health  of  the 
individual  exposed  to  the  gas. 

Relative  Rate  of  Absorption  by  Blood. — The  experiments 
of  Dr.  J.  S.  Haldane  and  others  have  shown  that  0.02  per 
cent,  of  carbon  monoxide  in  otherwise  pure  air  produces 
about  20  per  cent,  of  saturation  in  a  brief  period  of  time 
(20  min.?).  Since  pure  air  contains  20.9  per  cent,  of  oxygen, 
the  ratio  of  carbon  monoxide  to  oxygen,  in  the  air  breathed, 
is  2:2090,  or  1:1045.  But  the  ratio  of  absorption,  carbon 
monoxide  to  oxygen,  in  this  case,  is  20  :80,  or  1  :4,  the  blood 
showing  only  20  per  cent,  carbon  monoxide  and  80  per  cent, 
oxygen.  Hence,  the  relative  rate  of  absorption  by  the  blood, 
carbon  monoxide  to  oxygen,  is  about  260:1,  since  104,5^4  = 
say  260.  In  other  words,  the  blood  in  this  experiment  ab- 
sorbed carbon  monoxide  about  260  times  as  rapidly  as  it  ab- 
sorbed oxygen,  under  the  same  conditions. 

Another  experiment  showed  50  per  cent,  saturation  in 
the  blood  when  the  air  breathed  contained  0.08  per  cent,  of 
carbon  monoxide.  In  this  case,  the  ratio  of  carbon  monoxide 
to  oxygen  in  the  air  breathed  is  8  : 2090,  or  1 : 260.  But  the 
corresponding  ratio  of  absorption  is  1:1,  the  blood  showing 
50  per  cent,  of  saturation,  or  equal  quantities  of  these  two 


MINE  CrASES  105 

gases.  Hence,  in  this  case  also,  the  relative  rate  of  absorp- 
tion of  carbon  monoxide  and  oxygen  is  the  same  as  before, 
namely,  260:1. 

Another  experiment  showed  50  per  cent,  saturation  in  the 
blood  when  the  air  breathed  contained  0.05  per  cent,  of 
carbon  monoxide.  Here  the  ratio  of  carbon  monoxide  to 
oxygen  in  the  air  breathed  being  5  :2090,  or  1  :418,  and  the 
ratio  of  absorption,  as  before,  1:1,  the  relative  rate  of  ab- 
sorption is  418:1,  showing  that  the  blood  absorbed  carbon 
monoxide,  in  this  case,  about  400  times  as  rapidly  as  it  ab- 
sorbed oxygen,  under  like  conditions,  in  the  two  previous 
experiments. 

The  experiments  suggest  not  only  the  variation  in  the 
rapidity  of  the  absorption  of  carbon  monoxide  by  the  blood 
of  different  individuals,  with  varying  constitutions  and  de- 
grees of  health;  but  show  clearly  the  great  affinity  of  the 
haemoglobin  of  the  blood  for  carbon  monoxide  as  compared 
with  oxygen.  These  facts  demonstrate  forcibly  the  danger 
of  working  in  a  mine  atmosphere  containing  the  smallest 
possible  percentage  of  this  gas  even  when  the  worker  is  in 
robust  health. 

Production  of  Carbon  Monoxide  in  Mines. — Carbon  mon- 
oxide does  not  occur  naturally  in  mines,  but  may  be  and 
often  is  produced  in  dangerous  quantities  under  the  prac- 
tically unavoidable  conditions  and  occurrences  incident  to 
coal  mining. 

This  gas  is  produced  in  considerable  quantities  by  any 
combustion,  on  a  large  scale,  commonly  occurring  in  the 
limited  confines  of  mine  workings.  Examples  of  this  are 
mine  fires  and  explosions  of  gas  or  dust.  This  gas  is  also 
produced  by  the  explosion  of  powder  in  blasting.  It  is  pro- 
duced in  dangerous  quantities  by  the  slow  combustion  of 
fine  coal  and  slack  thrown  in  the  waste,  in  poorly  ventilated 
places  and  abandoned  areas  void  of  circulation.  Carbon 
monoxide  is  the  deadly  component  of  afterdamp,  which  renders 
the  latter  so  quickly  fatal  to  life,  as  shown  by  the  fatal  results 
that  follow  many  mine  explosions. 


106  MINE  GASES  AND  VENTILATION 

Detection  of  Carbon  Monoxide  in  Mines. — There  is  no  re- 
liable flame  test  for  the  detection  of  carbon  monoxide  as  it 
occurs  in  mines.  The  lamp  flame  is,  no  doubt,  lengthened 
when  fed  with  air  containing  the  gas,  but  this  effect  is  im- 
perceptible in  a  percentage  that  would  be  fatal  to  life. 

The  lengthening  of  the  flame  is  plainly  noticeable  when 
the  fine  dust  of  an  inflammable  coal  is  suspended  in  consid- 
erable quantity  in  the  still  air  of  a  mine  entry  or  chamber. 
This  is  the  result  of  the  increased  combustion  owing  to  the 
dust-laden  air  feeding  the  flame.  It  is  possible  that  a  barely 
perceptible  cap  may  be  discerned  at  times  under  particularly 
favorable  conditions.  This,  however,  would  be  a  dust  cap 
and  would  not  indicate  the  presence  of  the  gas. 

What  is  known  as  the  "blood  test"  will  reveal  the  pres- 
ence of  very  small  percentages  (0.01  per  cent.,  Haldane*)  in 
the  air.  The  delicacy  of  this  test,  however,  is  greatly  im- 
paired by  the  difficulty  of  correctly  judging  of  the  change  in 
the  color  of  the  blood  solution  employed  in  making  the  test. 
The  difficulty  is  increased  by  the  dim,  artificial  light  of  the 
mine  and  the  impaired  eyesight  and  possible  partial  color- 
blindness of  the  observer.  The  blood  test  also  requires  time 
and  care  in  its  making,  which  together  with  the  necessary 
apparatus  do  not  recommend  its  use  in  the  mine. 

The  experiments  of  Dr.  J.  S.  Haldanef  to  ascertain  the 
extent  to  which  animal  life  is  affected  by  the  presence  of 
carbon  monoxide  in  the  atmosphere  breathed  into  the  lungs 
led  him,  first,  to  suggest  the  use  of  small  animals  as  a  plainly 
visible  and  thoroughly  reliable  index  of  the  presence  of  gas 
in  quantity  dangerous  to  human  life.  Dr.  Haldane  observed 
that  mice  and  small  birds,  preferably  canaries,  were  pros- 
trated by  the  gas  in  a  much  briefer  period  than  is  required 
to  produce  the  same  effect  on  a  man. 

Exposed  to  an  atmosphere  containing  0.1  per  cent,  of 
carbon  monoxide,  a  mouse  became  giddy  in  12  min.,  while  a 
man  experienced  a  like  effect  only  after  breathing  the  same 
atmosphere  for  a  period  of  two  hours.  Again,  three  small 

*Trans.  I.  M.  E.,  Vol.  38,  p.  275. 
•jTrans.  I.  M.  E.,  Vol.  38,  pp.  267-280. 


MINE  GASES  107 

mice  and  a  canary  were  exposed  to  an  atmosphere  containing 
0.6  per  cent,  of  this  gas.  In  4  min.  the  canary  fell  from  its 
perch  and  died,  and  the  mice  became  helpless,  but  recovered 
quickly  in  fresh  air.  A  man  continued  to  breathe  the  same 
atmosphere  and,  at  the  expiration  of  10  min.,  was  unaffected, 
a  test  of  his  blood  showing  but  one-fourth  saturation. 

Dr.  Haldane's  conclusions,  based  on  his  experiments,  are 
briefly  as  follows: 

1 .  Noticeable  symptoms  are  never  produced  by  less  than 
about  0.02  per  cent,  of  carbon  monoxide  in  otherwise  pure 
air. 

2.  The  poisonous  effect  is  decreased  somewhat  by  a  mod- 
erate addition  of  carbon  dioxide;  but  increased  by  depletion 
of  the  oxygen  of  the  air. 

3.  Small  animals  recover  quickly  and  do  not  exhibit  the 
after  effects  of  the  poisoning  so  often  fatal  to  man. 

4.  The  analyses  of  the  blood  of  victims  of  the  afterdamp 
of  mine  explosions  usually  show  80  per  cent,  saturation. 

A  series  of  experiments  made  at  the  Pittsburgh  testing 
station  to  determine  the  effect  of  repeated  exposure  of  mice 
and  canaries  corroborates  the  conclusion  of  Dr.  Haldane  in 
respect  to  the  complete  rapid  recovery  of  these  small  animals 
from  the  effects  of  carbon-monoxide  poisoning. 

As  previously  explained,  men  who  have  been  once  over- 
come by  this  gas  are  more  sensitive  to  its  effects  again.  This 
is  not  the  case,  however,  with  mice  and  birds,  which  fact 
makes  them  the  more  useful  in  mining-  practice.  A  bird  or 
a  mouse  that  has  been  exposed  to  the  .gas  and-  overcome  a 
great  number  of  times  shows  no  more  sensitiveness  to  its 
poisonous  effects  than  one  never  poisoned  by  the  gas. 

Following  is  the  record  of  eight  exposures  of  a  canary  to 
an  atmosphere  containing  0.25  per  cent,  carbon  monoxide,  as 
given  on  p.  8,  Technical  Paper  62,  of  the  U.  S.  Bureau  of 
Mines,  each  exposure,  except  the  last,  being  made  immedi- 
ately upon  the  recovery  of  the  bird  from  the  previous  one. 
The  table  shows  the  time,  in  minutes  intervening  between  the 
moment  of  exposure,  first  signs  of  distress,  collapse  of  the 
bird  and  recovery  in  fresh  air. 


108  MINE  GASES  AND  VENTILATION 

TABLE  1. — EFFECT  OF  REPEATED  EXPOSURE  ON  CANARY 


Time  in  minutes 

M          f 

Distress 

Collapse 

Recovery 

1 

3 

1 

7 

2 

3 

1 

8 

3 

1 

3 

8 

4 

2 

3 

7 

5 

2 

2 

7 

6 

2 

2 

7 

7 

2 

1 

12 

(a  2-min.  interval) 
1  I  1 


The  above  record  shows  earlier  signs  of  distress  after  the 
first  two  exposures.  This  may  naturally  be  attributed  to  the 
alarm  and  expectancy  of  the  bird  arising  from  its  previous 
experience;  but  the  total  interval  to  collapse  was  uniform  (4 
min.),  except  in  the  fourth  and  the  two  last  exposures,  which 
were  5,  3  and  2  min.,  respectively. 

The  following  table  shows  the  same  data  recorded  in  four 
successive  exposures  of  a  mouse  to  a  0.3-per  cent,  mixture  of 
carbon  monoxide  and  pure  air: 

TABLE  2. — EFFECT  OF  REPEATED  EXPOSURE  ON  MOUSE 


Time  in  minutes 


No.  of  exposure 


Distress 

Collapse 

Recovery 

1 

3 

6 

17 

2 

3 

10 

23 

3 

4 

12 

34 

4 

3 

14 

not  given 

A  similar  series  of  experiments,  performed  by  exposing  a 
canary  at  irregular  intervals  and  on  different  days  to  at- 
mospheres containing  from  0.18  to  0.24  per  cent,  of  carbon 
monoxide  and  numbering  14  exposures  in  all,  extending  over 
a  period  of  nine  days,  showed  practically  the  same  results. 


MINE  GASES  109 

CARBON  DIOXIDE 

This  gas,  often  called  "carbonic  acid  gas"  or  "chokedamp" 
is  a  colorless  and  odorless  gas,  having  a  distinctly  acid  taste. 
It  is  not  combustible  and  will  not  support  combustion  in  any 
ordinary  form. 

How  Produced. — Carbon  dioxide  is  the  product  of  the  com- 
plete combustion  of  carbon  or  carbonaceous  matter  in  a 
plentiful  supply  of  air  or  oxygen.  It  is  produced,  in  mines, 
by  the  breathing  of  men  and  animals;  burning  of  lamps; 
explosion  of  powder  slow  combustion  of  fine  coal  and  slack 
in  the  gob;  and  other  forms  of  combustion  taking  place. 

Effect  on  Flame. — Carbon  dioxide  has  a  similar  effect  on 
flame  to  that  caused  by  an  exces  of  nitrogen;  or,  what  is  the 
same  thing,  a  dep  etion  of  oxygen  in  the  air.  The  presence  of 
carbon  dioxide  in  the  air  tends  to  reduce  the  activity  of  com- 
bustion. It  dims  the  flame  of  a  lamp  and  extinguishes  it 
when  present  in  sufficient  quantity. 

The  percentage  of  carbon  dioxide  that  will  extinguish 
flame  depends  on  both  the  nature  of  the  flame  and  the  amount 
of  oxygen  in  the  air  feeding  the  flame.  A  gas-fed  flame,  as  the 
hydrogen  flame  of  the  Clowes  lamp,  or  the  acetylene  flame  of 
a  carbide  lamp,  is  less  susceptible  to  extinction  from  this 
cause  than  is  an  oil-fed  flame. 

The  flame  of  a  lamp  burning  sperm  or  cottonseed  oil  is 
extinguished  in  an  artificial  atmosphere  (which  is  the  usual 
condition  in  a  mine)  containing  14  per  cent,  of  carbon  dioxide. 
But,  in  a  residual  atmosphere  formed  by  allowing  the  lamp 
to  burn  in  a  closed  place  till  extinguished,  only  3  per  cent, 
of  carbon  dioxide  is  required  for  extinction  of  the  flame. 

Effect  on  Life. — Carbon  dioxide  is  not  classed  as  one  of  the 
poisonous  mine  gases,  although  it  exerts  a  toxic  effect  on  the 
human  system.  It  is  irrespirable  when  unmixed  with  air  and 
if  breathed  produces  death  by  suffocation.  In  smaller  quan- 
tities, it  causes  headache,  nausea  and  pains  in  the  back  and 
limbs. 

According  to  Dr.  Haldane,  no  appreciable  effect  is  pro- 
duced by  breathing  air  containing  carbon  dioxide,  until  there 


110  MINE  GASES  AND  VENTILATION 

is  about  3  per  cent,  of  this  gas  present.  Breathing  then 
becomes  slightly  more  difficult;  5  or  6  per  cent,  of  the  gas 
causes  deckled  panting;  and  18  per  cent,  suffocation  and  death. 
The  effect  of  the  gas  is  much  increased  if  the  oxygen  content 
of  the  air  is  below  the  normal. 

For  example,  with  18  per  cent,  carbon  dioxide  present, 
there  is  0.209  (100  -  18)  =  17.14  per  cent,  oxygen  and  0.791 
(100  —  18)  =  64.86  per  cent,  nitrogen,  under  normal  con- 
ditions. This  is  a  fatal  atmosphere. 

But,  if  the  oxygen  of  the  air  has  been  depleted  so  that 
the  ratio,  oxygen  :  nitrogen,  is  less  than  20.9  :  79.1;  then  a  less 
percentage  of  carbon  dioxide  than  that  named  above  (18%) 
would  be  fatal  to  life. 

Treatment  when  Overcome. — Remove  promptly  to  fresh 
air;  apply  alternately  cold  and  lukewarm  bandages  to  the 
chest;  rub  the  limbs  and  body  briskly  to  start  circulation;  and, 
if  necessary,  use  artificial  respiration.  When  consciousness 
is  restored  put  the  patient  to  bed  and  keep  him  quiet  for 
several  days. 

BLACKDAMP 

It  is  a  common  mistake,  in  mining  practice,  to  regard  car- 
bon dioxide  as  another  name  for  "blackdamp,"  which  is  found 
in  such  quantities  in  many  poorly  ventilated  mines.  Carbon 
dioxide  is  one  constituent  only  of  blackdamp. 

The  term  blackdamp  describes  a  variable  mixture  of  air 
deficient  in  oxygen,  and  carbon  dioxide.  It  consists  therefore 
of  carbon  dioxide,  nitrogen  and  oxygen,  in  varying  quantities. 
The  percentage  of  oxygen  in  the  mixture  will  determine  its 
respirable  quality.  The  nitrogen  is  wholly  inert  and  acts 
only  to  dilute  the  mixture  and  thus  reduce  the  percentage  of 
oxygen  present.  The  carbon  dioxide  not  only  dilutes  the  mix- 
ture but  produces  also  a  toxic  effect  on  the  human  system, 
although  this  effect  is  not  of  such  a  nature  as  to  class  carbon 
dioxide  as  a  poisonous  gas. 

The  production  of  blackdamp  in  coal  mines  is  due  to  two 
chief  causes:  1.  The  absorption  of  the  oxygen  of  the  air  by  the 
coal.  2.  The  generation  of  carbon  dioxide  by  the  various 


MINE  GASES  111 

forms  of  combustion  or  oxidation  continually  taking  place 
in  the  workings  of  the  mine. 

The  absorption  of  oxygen  from  the  mine  air  by  the  freshly 
exposed  surfaces  of  coal  is  more  rapid  than  what  is  generally 
supposed.  Experiment  has  shown  that  a  certain  freshly 
mined  bituminous  coal  absorbed  from  one-eighth  to  one- 
seventh  of  its  volume  of  oxygen  from  the  surrounding  air,  in 
24  hr.;  while  only  about  one-tenth  of  this  oxygen  was  con- 
verted into  carbon  dioxide.  It  is  suggested  that  the  remain- 
ing nine-tenths  of  the  oxygen  absorbed  unites  chemically  with 
certain  un saturated  hydrocarbons  in  the  coal. 

The  effect  of  this  rapid  absorption  of  oxygen,  in  the  still 
air  of  badly  ventilated  places,  in  coal  mines,  as  can  be  readily 
imagined,  is  to  deplete  the  oxygen  content  of  the  air.  This  is 
especially  the  case  where  tons  of  coal  are  shot  down  at  night 
and  left  to  be  loaded  out  the  following  day  and  the  ventila- 
tion during  the  night  is  much  diminished  in  the  mine. 

On  the  other  hand,  where  the  ventilation  is  adequate  and 
there  is  still  blackdamp  produced  in  quantity,  it  is  the  result 
of  the  generation  of  carbon  dioxide  from  some  cause,  gen- 
erally a  mine  fire  or  the  slow  combustion  of  fine  coal. 

AFTERDAMP 

The  term  " afterdamp,"  as  the  word  implies,  is  used  to 'de- 
scribe the  variable  mixture  of  noxious  gases  that  remains 
after  any  explosion  of  gas,  dust  or  powder  in  a  mine. 

Composition. — It  is  impossible  to  give  the  composition  of 
afterdamp,  except  in  the  most  general  way;  because  the 
gases  formed  depend  on  so  many  varying  conditions,  in  respect 
to  the-  character  of  the  gas  or  dust  burned ;  the  relative  vol- 
ume of  available  oxygen;  the  size  of  the  workings  where  the 
explosion  takes  place,  as  determining  the  temperature  and 
pressure  developed;  and  the  condition  of  the  mine  with  respect 
to  gas,  dust  and  moisture. 

Afterdamp  may  contain  variable  quantities  of  nitrogen, 
carbon  dioxide,  carbon  monoxide,  water  vapor  and,  at  times, 
lesser  amounts  of  nitrous  oxide  gas  and  possibly  some  un- 


112  MINE  GASES  AND  VENTILATION 

burned  methane.     The  mixture  is  extremely  dangerous,  being 
fatal  to  life  and  often  highly  explosive. 

INFLAMMABLE  AND  EXPLOSIVE  MINE  GASES 

The  presence  of  combustible  gases  in  the  atmosphere  of 
a  mine  is  always  an  element  of  danger  for  three  principal 
reasons.  1.  The  percentage  of  gas  in  the  mine  air  may  be 
sufficient  to  form  an  explosive  mixture  known  as  firedamp. 
2.  The  temperature  of  ignition  of  most  of  these  gases  is  lower 
than  that  of  methane,  which  is  usually  the  chief  constituent 
of  firedamp,  and  the  latter  is  rendered  more  readily  ignitable 
by  reason  of  their  presence.  3.  The  presence  of  the  smallest 
percentage  of  a  combustible  gas  assists  to  that  extent  the 
ignition  of  a  dust-laden  atmosphere,  and  increases  the  vio- 
lence of  its  explosion  when  ignited. 

The  Inflammable  Gases. — The  inflammable  or  combustible 
mine  gases,  in  the  order  of  their  importance,  are  methane 
(CH4),  carbon  monoxide  (CO),  ethane  (C2H6),  ethene  or  olefi- 
ant  gas  (C2H4),  hydrogen  (H2)  and  hydrogen  sulphide  (H2S). 
Each  of  these  gases  is  not  only  combustible  but  forms  an  ex- 
plosive mixture  when  mixed  with  air  in  certain  proportions. 

Inflammable  Range  of  Gases. — The  combustion  of  an  in- 
flammable gas,  under  mining  conditions,  requires  the  presence 
of  air  or  available  oxygen.  The  relative  proportion  of  air  and 
gas  in  the  mixture  determines  the  character  and  completeness 
of  the  combustion  and  the  range  of  inflammability  of  the  gas. 

The  maintenance  of  flame  throughout  a  gaseous  mixture 
requires  that  the  heat  of  combination  between  the  combusti- 
ble and  the  atmosphere  supporting  the  combustion  shall  be 
equal  to  that  lost  by  radiation,  conduction  and  absorption  by 
the  air  and  gaseous  products  formed.  Two  conditions  are 
possible. 

1.  The  proportion  of  gas  to  air  may  be  such  as  to  give  a 
low  rate  of  combination  and  a  correspondingly  small  genera- 
tion of  heat,  which  is  insufficient  to  raise  the  adjacent  gas- 
eous molecules  to  an  equal  temperature,  resulting  in  a  still 
lower  rate  of  combination  and  a  lesser  generation  of  heat 
as  the  action  proceeds  through  the  mass  till  it  finally  ceases. 


MINE  GASES  113 

2.  Again,  the  proportion  of  air  to  gas  may  be  such  as  to 
cause  an  absorption  of  heat  greater  than  that  generated  when 
the  condition  will  likewise  be  a  falling  one  and  there  can 
result  no  general  extension  of  flame  throughout  the  mass. 

The  first  of  these  two  conditions  (excess  of  gas)  deter- 
mines the  higher  inflammable  limit  of  the  gas,  while  the 
second  condition  mentioned  (excess  of  air)  marks  the  lower 
inflammable  limit.  Beyond  these  two  limits  the  gaseous 
mixture  is  not  inflammable.  In  mining  practice,  mixtures 
above  the  higher  limit  are  more  dangerous  than  those  below 
the  lower  limit,  as  more  air  will  make  them  explosive. 

Explosive  Range  of  Gases. — A  combustible  gas  is  always 
inflammable  in  proportions  of  gas  to  air  outside  of  the  ex- 
plosive range  of  the  gas.  In  other  words,  the  range  of 
inflammability  is  wider  than  and  embraces  the  range  of  ex- 
plosibility.  The  same  principles,  however,  apply  in  respect 
to  each  of  these  conditions. 

The  degree  of  explosiveness  of  a  gaseous  mixture  is  in- 
creased as  the  rate  of  combination  is  more  rapid  and  the  loss 
of  heat  less;  or  decreased  as  the  rate  of  combining  is  slower 
and  the  loss  of  heat  greater. 

Maximum  Explosive  Point. —  It  is  quite  generally  assumed 
that  the  maximum  explosive  force  of  a  gas  is  developed 
when  the  proportion  of  air  or  oxygen  is  just  sufficient  for 
the  complete  combustion  of  the  gas.  While  this  is  sufficiently 
close  for  all  practical  purposes,  it  is  stated  (Emich)  that  the 
explosibility  is  not  necessarily  greatest  at  this  point. 

Inflammable  and  Explosive  Limits. — The  following  table 
gives  the  lower  and  higher  inflammable  and  explosive  limits 
and  the  maximum  explosive  point  of  the  three  most  important 
combustible  mine  gases,  except  only  the  higher  inflammable 
limit  of  carbon  monoxide,  which  has  not  been  determined,  but 
is  probably  about  80  per  cent.  The  table  shows  the  percent- 
age of  gas  present  in  the  mixture,  at  each  of  the  five  stages 
given.  The  lower  inflammable  limit  and  the  maximum 
explosive  point  have  been  calculated  for  each  of  these  gases, 
while  the  other  data  are  the  results  of  experiment.  A  normal 
condition  of  the  air  is  assumed : 


114 


MINE  GASES  AND  VENTILATION 


TABLE    GIVING   THE    INFLAMMABLE    AND   EXPLOSIVE   LIMITS   AND   THE 

MAXIMUM  EXPLOSIVE  POINT  OF  METHANE,  HYDROGEN  AND 

CARBON  MONOXIDE 


Gas 

Lower 
inflam. 
limit 

Lower 
explo. 
limit 

Maximum 
explo. 
point 

Higher 
explo. 
limit 

Higher 
inflam. 
limit 

Methane  ;       4.5              7.1             9.5           16.7          20.5 

Carbon  monoxide  8.4 

16.5 

29.5 

75.0 

Hydrogen  5  .  0 

9.5 

29.5 

66.3 

72.0 

The  same  data,  in  reference  to  olefiant  gas  (ethene  or  ethy- 
lene),  C2H4, are:  Lower  explosive  limit, 4.0  per  cent.;  maximum 
explosive  point,  6.5  per  cent.;  and  higher  explosive  limit,  22 
per  cent.  These,  however,  have  only  a  relative  importance 
in  respect  to  mining,  because  the  percentage  of  this  gas  pres- 
ent in  mines  is  very  small. 

Peculiarities  of  Explosion. — A  peculiarity  in  the  explosion 
of  a  mixture  of  methane  and  air  is  that,  at  the  temperature  of 
ignition  (1200°F.),  about  10  sec.  are  required  before  the  gas 
will  ignite  (Mallard  and  Le  Chatelier),  while  both  hydrogen 
and  carbon  monoxide  ignite  at  once,  upon  contact  with  the 
flame.  The  time  required  for  the  ignition  of  methane  grows 
rapidly  less  as  the  temperature  is  increased. 

The  same  authorities  also  claim  that  mixtures  of  methane 
and  air  in  any  proportion  are  explosive  at  high  temperatures, 
and  the  same  effect  has  been  observed  at  high  pressures.  In 
other  words,  an  increase  of  temperature  or  pressure  has  the 
effect  to  widen  the  explosive  range  of  a  gas 

A  mixture  of  carbon  monoxide  and  air  will  not  explode  in 
the  absence  of  moisture.  The  explosion,  in  this  case,  seems 
to  require  two  stages,  the  carbon  monoxide  taking  the  oxygen 
from  the  water,  which  is  replaced  immediately  by  the  oxygen 
of  the  air,  as  represented  by  the  following  equations: 


and 


CO  +  H2O  =  CO2  +  H2 
2H2  +  O2  =  2H2O 


It  has  been  argued  that,  since  carbon  monoxide,  which  is 
distilled  from  coal  dust  floating  in  the  mine  air,  is  not  ex- 


MINE  CASES 


115 


plosive  in  dry  air,  the  safest  condition  is  a  dry  mine  atmos- 
phere, which,  however,  is  practically  impossible. 

Explosive  Mine  Gases. — The  diagram,  Fig.  13,  given  below 
combines,  in  a  compact  form,  most  of  the  important  reactions 
and  data,  relating  to  the  combustion  and  explosion  of  those 
mine  gases  that  form  explosive  mixtures  with  air.  In  the  upper 
left-hand  corner  is  a  graphic  illustration  of  the  relative  extent 


E3  Inflammable  lont 
2!?5  [xplosive  lone  . 
;__  Maximum  t*p!osi*t  point 

tuphwe  Limh 

inflammable  Limih 

-—  Life  Line  (fatal  Per  Cent ) 


EQUAL    W 

CONSTANT 


_ 

3.4090 


©AS 


EQUATION  SNOWING  COMBUSTION 
•OF  6AS  IN  OXYGtN 


HEAT  0>  COMBUSTION 

IN  OXY6EN 
6.TU   P£R  POUND 


[THYLCNl 
OLtFIANl  6A$ 


UK  BON  MONO/UN 
C AH  BO  NIC  OJTIOf 


>S  14 


0.967 


HOUCOIM  WE/6HT 

JHLATIVf  VOLUME         I 

REACTION  2CO 1 0,  •  2CO, 


KllATIVl  VOLUMf 


2      I 


URMPTOCO, 
4.32S      ' 


VOCS3 


HfDffOCEH  SULPHID[ 
WLPHURCTtl)  HYDKOMN 


34  17  \  1 .91?  \OJ9t?     iO.St> 


Rt 'ACTION  2H,tO,'  2H.O 
HOLECULAK  WEIGHT  4     3Z      36 

RELATIVE  Wfl6HT  169 

RELATIVE  VOLUME  2      I ?    _ 

REACTION  Z^JCV,?.;^?^ 

MOIKUIAR  WEIGHT  66        36      Of    J6 

KHATIVC  MIGHT  n      »     j?    9 

RELAT/Vf  VOLUME  2322 


BUKNEDTOHtO 

AT  32* f 

62.03Z 


H,OAT  32T 
7.J19 


FIG.   13. 

of  the  explosive  and  inflammable  zones  of  each  of  these  gases 
when  mixed  with  air.  The  horizontal  lines,  in  each  gas  col- 
umn, mark,  approximately,  the  maximum  explosive  point  and 
the  lower  and  upper  explosive  and  inflammable  limits;  also 
the  fatal  percentage  is  indicated  by  the  dotted  lines.  These 
marks  are  explained  by  the  legend  in  the  upper  right-hand 
corner  The  specific  heats  are  given  for  equal  weights  of 
the  gases,  for  constant  volume  and  constant  pressure,  referred 
to  water  as  unity. 


SECTION  IV 
EXPLOSIONS  IN  MINES 

DEFINITION,  GAS  EXPLOSION,  DUST  EXPLOSION— INFLAMMA- 
TION OF  GAS — NATURE  AND  TEMPERATURE  OF  FLAME — 
EXPLOSION  OF  GAS — COAL  DUST,  ITS  INFLAMMABILITY 
AND  INFLUENCE,  EFFECT  OF  STONE  DUST — MINE  EXPLO- 
SION, DEVELOPMENT,  CAUSES,  MIXED  LIGHTS,  ELECTRIC 
MINE  LAMPS,  PREVENTION  OF  MINE  EXPLOSIONS. 

Definition. — A  mine  explosion  is  understood  to  be  a  violent 
disturbance  of  the  atmosphere  within  a  mine,  as  manifested 
by  a  destructive  blast  or  rush  of  air  accompanied  by  more  or 
less  flame,  and  is  the  result  of  the  ignition  and  combustion 
with  explosive  rapidity  of  gas  and  dust  or  either  accumulated 
in  the  mine. 

Gas  Explosion. — An  explosion  produced  and  maintained 
chiefly  by  gas  accumulated  in  the  mine  workings  and  passages 
or  mixed  with  the  air  current  is  described  as  a  "gas  explosion," 
although  practically  every  mine  explosion  involves  the  com- 
bustion of  both  gas  and  dust. 

Dust  Explosion. — An  explosion  in  which  the  fine  coal  dust 
accumulated  in  the  mine  or  suspended  in  the  air  current 
plays  a  prominent  part  is  commonly  called  a  "dust  explosion," 
although  it  may  have  originated  in  a  local  explosion  of  gas, 
which  is  true  of  most  mine  explosions. 

Few  if  any  mine  explosions  are  wholly  due  to  gas  or  dust, 
but  combine  both  of  these  elements  in  varying  proportions 
the  character  of  the  explosion  as  "gas"  or  "dust"  being  deter- 
mined by  the  later  evidences. 

INFLAMMATION  OF  GAS 

Theory  of  Inflammation. — The  inflammation  of  a  combus- 
tible gas  involves,  at  least,  two  main  conditions  that  are 
essential  to  the  reactfon.  They  are  as  follows : 

116 


EXPLOSIONS  IN  MINES 


117 


1.  The  presence  of  another  gas  that  will  support  the  com- 
bustion by  reason  of  the  different  affinities  of  the  elements 
of  the  gases  that  invite  dissociation  and  recombination  to 
form  other  compounds. 

2.  A  rise  of  temperature,  at  the  point  of  contact  of  the 
two  gases,  sufficient  to  start  the  reaction. 

The  ignition  of  a  combustible  gas  in  some  cases  (carbon 
monoxide)  requires,  besides  the  above,  the  presence  of  water 
vapor. 

Temperature  of  Ignition. — At  the  same  pressure  and  under 
the  same  conditions  of  ignition,  the  temperature  at  which  a 
given  gas  inflames  or  the  temperature  of  ignition  for  that  gas 
is  fixed.  The  following  table  gives  the  average  temperatures 
of  ignition  of  the  principal  mine  gases,  as  determined  by 
experiment: 

AVERAGE  TEMPERATURES  OF  IGNITION  OF  THE  COMBUSTIBLE  MINE 
GASES  IN  NORMAL  AIR 


Gas 

Symbol 

Temperature 
of  ignition 
(deg.  F.) 

Carbon  monoxide      .    .      

CO 

1240 

Methane  .                                     

CH4 

1212 

Ethane 

C2H6 

1140 

Ethene  (olefiant  gas)     

C2H4 

1124 

Hydrogen                                  .        

H2 

1077 

Acetylene 

C2H2 

970 

NATURE  AND  TEMPERATURE  OF  FLAME 

The  Nature  of  Flame. — Flame,  as  here  considered,  is  burn- 
ing gas.  It  may  be  luminous  or  nonluminous,  according  to  the 
presence  or  absence  of  carbon  either  free  or  combined  as 
hydrocarbons.  The  incandescence  of  the  carbon  particles 
when  present  renders  the  flame  luminous.  This  is  the  case 
with  most  oil-fed  flames  and  flames  burning  in  a  dusty  atmos- 
phere. The  flame  of  hydrogen  burning  in  clear,  pure  air  is 
practically  nonluminous.  Methane  produces  an  almost  non- 


118  .         MINE  GASES  AND  VENTILATION 

luminous  flame,  but  the  flame  of  the  heavy  hydrocarbon  gases 
is  always  more  or  less  luminous. 

The  Temperature  of  Flame. — The  temperature  of  flame  is 
variable,  owing  to  numerous  conditions  that  affect  the  com- 
bustion of  the  gas  both  as  to  its  rapidity  and  completeness. 
The  temperature  will  vary  in  different  parts  of  the  same 
flame,  because  of  a  variable  supply  of  air  that  not  only  affects 
the  combustion  of  the  gas  but  absorbs  much  of  the  heat  de- 
veloped and  lowers  the  temperature  of  the  flame. 

Owing  to  these  varying  conditions  it  is  clearly  impossible 
to  calculate  the  actual  flame  temperature  of  a  burning  gas. 
This  is  often  roughly  assumed  to  be  about  one-half  of  the 
theoretical  value  as  calculated  from  the  heat  of  combustion 
per  pound  of  gas  and  the  heat  absorbed  by  the  corresponding 
products  of  combustion,  for  each  degree  rise  in  temperature. 

It  is  important  not  to  confuse  the  flame  temperature  of  a 
combustible  gas  with  its  temperature  of  ignition,  as  they 
have  no  connection  with  each  other. 

Calculation  of  the  Theoretical  Flame  Temperature. — The 
theoretical  temperature  of  the  flame  of  a  burning  gas  is  the 
highest  possible  temperature  that  results  from  its  complete 
combustion,  assuming  (what  is  never  the  case  in  an  open- 
burning  flame)  that  only  sufficient  air  is  present  for  the  com- 
plete combustion  of  the  gas. 

There  is  always  an  excess  of  air  in  the  outer  envelope  or 
zone  of  a  flame  exposed  to  the  air,  and  this  excess  of  air  beyond 
what  is  required  for  the  combustion  absorbs  heat  and  lowers 
the  temperature  of  the  flame  in  the  outer  zone. 

The  temperature  within  or  in  the  body  of  the  flame  more 
nearly  approaches  the  theoretical  maximum,  which  can  be 
calculated.  This  maximum  temperature  is  found  by  dividing 
the  total  heat  of  combustion  above  32  deg.  F.,  per  pound  of 
combustible,  less  the  heat  rendered  latent  in  the  water  vapor 
produced,  by  the  heat  required  to  raise  the  temperature  of 
the  products  of  combustion  one  degree.  The  quotient  ob- 
tained gives  the  rise  of  temperature  above  32  deg.  F.,  which 
must  therefore  be  added  in  order  to  find  the  theoretical  tem- 
perature of  the  flame. 


EXPLOSIONS  IN  MINES  110 

Flame  Temperature  ot  Methane  Burning  in  Air. — The  first 
portion  of  the  process  is  similar  to  that  explained  in  the 
calculation  of  the  lower  inflammable  limit  of  methane  and 
need  not  be  repeated  here.  It  was  found  that  for  every 
pound  of  methane  burned  there  was  produced  carbon  dioxide, 
'  2%  lb.;  water  vapor,  2K  lb.;  and  nitrogen,  13.39  Ib.  So  far 
the  two  operations  are  the  same.  (Page  96.) 

As  before,  one  pound  of  methane,  burning  to  carbon  dioxide 
and  water  at  32  deg.  F.,  develops  23,513  B.t.u.  From  this 
must  be  subtracted  the  heat  required  to  convert  2%  lb.  of 
water  at  32  deg.  into  steam  at  212  deg.,  which  is  absorbed  in 
the  formation  of  the  water  vapor;  thus, 

23,513  -  2>i  (212  -  32  +  970.4)  =  20,924.6  B.t.u. 

The  result  obtained  is  the  net  heat  available  for  raising  the 
temperature  of  the  products  of  combustion,  which  constitute 
the  larger  portion  of  the  body  of  the  flame. 

It  is  necessary  now  to  calculate  the  heat  required  to  raise 
the  temperature  of  the  respective  weights  of  the  products  of 
combustion  one  degree.  The  weight  of  each  of  these  products, 
as  previously  given,  is  multiplied  by  its  specific  heat  for 
constant  pressure  and  the  sum  of  these  products  is  the  total 
heat  required  for  each  degree  of  rise  in  temperature;  thus, 

Sp.  heat         Weight         B.t.u. 

Carbon  dioxide 0.2163  X    2.75  =  0.5948 

Water  vapor 0 . 4805  X    2 . 25  =  1 . 0811 

Nitrogen 0.2438  X  13.39  =  3.2645 


Heat  absorbed,  per  degree  rise ...  4 . 9404 

Finally,  the  rise  of  temperature  in  the  body  of  the  flame 
that  is  possible,  in  this  case,  assuming  that  all  of  the  heat 
developed  is  absorbed  by  the  products  of  the  combustion  only, 
is  as  follows: 

Rise  of  temperature,  20,924.6  -5-  4.9404  =  4235  deg.  F. 

This  rise  of  temperature,  like  the  heat  developed  by  the 
combustion,  is  estimated  from  32  deg.  F.  The  theoretical 
flame  temperature  is  therefore  4235  +  32  =  4267  deg.  F. 


120  MINE  GASES  AND  VENTILATION 

Flame  Temperature  of  Carbon  Monoxide.  —  The  first  step 
in  calculating  the  flame  temperature  of  this  gas  is  to  write 
the  chemical  equation  expressing  the  reaction  that  takes  place 
when  carbon  monoxide  burns  to  carbon  dioxide,  ignoring  for 
the  present  the  nitrogen  in  the  air;  thus, 

2CO  +  O2  =  2CO2 

Molecular  weights,  56         32  =  88 

Relative  weights,  1         %       l% 

Since  oxygen  forms  23  per  cent,  of  normal  air,  by  weight, 
and  nitrogen  77  per  cent.,  the  ratio  of  nitrogen  to  oxygen  is 
77  :  23,  and  the  relative  weight  of  nitrogen  involved  here  is 

4       77       44 


Hence,  for  every  pound  of  carbon  monoxide  burned,  there  is 
produced  carbon  dioxide,  l%  lb.;  and  nitrogen,  1.91  Ib. 

The  heat  of  combustion  of  carbon  monoxide  burning  to 
carbon  dioxide,  as  taken  from  a  table  giving  the  heat  of  com- 
bustion of  various  substances,  is  4325  B.t.u.  per  lb.  of  gas 
burned.  There  being  no  water  vapor  formed  in  this  reaction, 
the  above  is  the  actual  heat  available  for  raising  the  tempera- 
ture of  the  products  of  the  combustion,  which  form  the  body 
of  the  flame,  disregarding  radiation  and  conduction  losses. 

Now,  calculating,  as  before,  the  heat  required  to  raise  the 
temperature  of  the  respective  weights  of  the  products  of  this 
combustion  one  degree,  by  multiplying  the  weight  of  each 
product  by  its  specific  heat  for  constant  pressure  and  finding 
the  sum  of  those  products,  we  have 

Sp.  heat      Weight          B.t.u. 

Carbon  dioxide  ...................   0.2163  X  11/7  =  0.3399 

Nitrogen  ......  .  ..................   0.2438  X  1.91  =  0.4657 


Heat  absorbed,  per  degree  rise ....  0 . 8056 

The  resulting  rise  of  temperature  above  32  deg.  F.,  in  the 
body  of  the  flame,  which  determines  the  theoretical  flame  tem- 
perature, is  then  4325  -r-  0.8056  =  5369  deg.  F.  and  the  corre- 
sponding temperature,  5369  +  32  =  say  5400  deg.  F. 


EXPLOSIONS  IN  MINES  121 

Although  the  presence  of  moisture  (water  vapor,  H2O)  is 
necessary  to  the  ignition  of  carbon  monoxide,  it  is  not  re- 
quired to  take  this  into  account  in  making  the  above  calcu- 
lation, for  the  reason  that  the  heat  of  dissociation  is  balanced 
by  the  heat  of  recombination  in  the  molecule  of  water  and  no 
loss  of  heat  is  assumed  to  occur.  It  has  been  suggested  that 
the  water  only  serves  to  start  the  reaction  by  effecting  the 
ionization  of  the  elements. 

The  theoretical  flame  temperature  as  calculated  above, 
however,  both  for  methane  and  carbon  monoxide,  is  consid- 
erably modified  by  the  humidity  of  the  air  supporting  the 
combustion. 

Volume  of  Flame. — It  is  frequently  estimated  roughly  that 
the  volume  of  a  flaming  gas  is  proportional  to  its  absolute 
temperature.  For  example,  assuming  the  original  tempera- 
ture of  the  gas  as  0  deg.  F.,  the  theoretical  flame  volumes  of 
methane  and  carbon  monoxide  are,  respectively, 

Methane,  460  -f-  4267  -r-  460  =  say,  10      volumes. 

Carbon  monoxide,     460  +  5400  -r-  460  =  say,  12%  volumes. 


EXPLOSION  OF  GAS 

Influence  of  Temperature  on  Explosion. — A  rise  of  the 
initial  temperature  of  an  explosive  mixture  slightly  extends 
the  lower  inflammable  limit,  but  has  no  appreciable  effect 
on  the  higher  limit,  owing  to  the  small  relative  value  of  the 
increase  as  compared  with  the  high  temperature  developed 
in  the  explosion. 

Influence  of  Pressure  on  Explosion. — Pressure  exerted  on 
an  explosive  mixture  increases  its  density  and  temperature 
and  renders  it  more  readily  igriitable.  In  other  words,  an 
increase  of  pressure  lowers  the  lower  inflammable  limit  of 
an  explosive  gaseous  mixture.  An  increase  of  pressure,  like- 
wise increases  the  velocity  of  propagation  of  explosion  in 
the  mixture,  raises  the  temperature  developed  and  extends 
the  higher  inflammable  limit.  In  other  words,  an  increase 
of  pressure  widens  the  explosive  range  of  a  combustible  gas. 


122  MINE  GASES  AND  VENTILATION 

Influence  of  Relative  Humidity  on  Explosion. — While  the 
presence  of  moisture  (water  vapor)  in  a  gaseous  mixture  is 
often  necessary  to  secure  its  explosion,  as  explained  in  ref- 
erence to  carbon  monoxide,  the  water  vapor  absorbs  much 
of  the  heat  and  lowers  the  temperature  developed,  thereby 
reducing  the  rate  of  combination  and  the  force  of  the  ex- 
plosion, except  where  fine  coal  dust  is  suspended  in  the  air, 
when  partial  dissociation  may  take  place  in  the  water  vapor 
and  result  in  increasing  the  energy  of  the  reaction. 

Influence  of  Catalysis  to  Cause  Explosion. — Catalysis  is 
the  effect  produced  by  a  foreign  substance  to  assist  chemical 
reaction  between  two  other  substances,  while  the  substance 
itself  undergoes  no  change — -first  discovered  by  Berzelius. 
Much  difference  of  opinion  exists  as  to  the  suggested  catalytic 
action  of  fine  incombustible  dust  suspended  in  mine  air,  to 
assist  the  explosion  of  combustible  gases.  Finely  powdered 
stone  dust  has  been  shown  to  retard  the  ignition  of  coal 
dust  by  mixing  with  and  diluting  the  latter.  This  effect, 
however,  is  wholly  physical  and  not  related  to  the  possible 
catalytic  action  referred  to  by  Sir  Frederick  Abel  and  others 
who  have  studied  the  subject  closely. 

Influence  of  Character  of  Initial  Impulse. — The  manner  in 
which  the  gas  is  ignited  or  the  character  of  the  initial  im- 
pulse determines  largely  the  explosion  of  gaseous  mixtures.  . 
For  example,  a  firedamp  mixture  ignited  by  a  lamp  flame 
may  not  explode,  while  if  fired  by  the  flame  of  a  blownout 
or  windy  shot,  the  greater  volume  and  intensity  of  the  flame 
may  cause  an  explosion. 

The  volume  of  the  flame  is  important,  because  it  envelops 
a  larger  portion  of  the  gaseous  mixture  and  ignition  is  thus 
started  generally  throughout  the  mass,  causing  a  greater 
development  of  heat  and  reducing  the  percentage  of  loss  by 
radiation,  convection  and  conduction. 

The  intensity  of  the  initial  impulse  or  the  higher  tem- 
perature of  the  igniting  flame  will  often  cause  the  explosion 
of  a  gaseous  mixture  that  would  burn  quietly  if  ignited  by 
a  less  intense  source  of  heat  energy.  The  dissipation  of  heat 
is  so  rapid  and  general  in  a  burning  gas  that  the  transition 


EXPLOSIONS  IN  MINES  123 

from  inflammation  to  explosion  requires  a  conservation  of 
heat  or  greater  local  energy  than  can  often  be  realized  in 
the  large  open  workings  of  a  well-ventilated  mine. 

COAL  DUST 

Influence  of  Coal  Dust  on  Explosion. — The  fine  dust  of  an 
inflammable  coal  when  floating  in  the  mine  air  may  render 
the  air  explosive  in  the  entire  absence  of  explosive  gas.  Under 
such  conditions,  however,  the  ignition  and  explosion  will 
only  take  place  when  the  floating  dust  is  acted  upon  by  a 
flame  of  considerable  volume  and  intensity. 

When  a  small  percentage  of  methane  is  present,  insufficient 
of  itself  to  make  the  air  explosive,  the  presence  of  the  dust 
floating  in  the  air  is  more  dangerous  than  when  no  gas  is 
present.  The  dust-laden  air  is  more  easily  ignited  and  the 
force  of  the  resulting  explosion  is  increased  in  proportion  to 
the  inflammability  of  the  mixture. 

The  purity,  fineness,  humidity  and  inflammability  of  the 
dust  are  important  factors  in  determining  the  character  of 
the  explosion,  since  these  with  oxygen  are  the  chief  elements 
that  promote  the  rapidity  of  the  combustion,  which  is  the 
necessary  condition  of  any  explosion. 

The  suspended  dust  feeds  the  flame  of  an  explosion  that 
is  started  in  a  mine,  and  thus  serves  to  propagate  the  blast 
and  extend  what  would  otherwise  have  proved  only  a  local 
explosion.  This  action  is  cumulative  in  a  dry  and  dusty 
mine.  The  dust  lying  on  the  roads  and  clinging  to  the  sides 
and  timbers  of  the  passageways  is  blown  into  the  air  by  the 
force  of  the  rushing  wind  that  precedes  the  explosive  wave, 
producing  what  has  well  been  called  a  "pioneering  cloud" 
of  dust  that  is  itself  highly  explosive. 

The  weight  of  fine  bituminous  coal  dust  required  to  render 
normal  air  explosive  has  been  variously  estimated.  Tests 
made  at  the  Pittsburgh  Experiment  Station-  with  dust  from 
a  200-mesh  sieve  showed  explosion  took  place  in  a  density  of 
32  grm.  per  cu.  m.  (0.032  oz.  per  cu.  ft.)  or,  say  1  Ib.  of  dust 
in  500  cu.  ft.  of  air.  The  Taffanel  experiments  (Lievin)  gave 
explosion  in  70  grm.  per  cu.  m.  (0.07  oz.  per  cu.  ft.)  or,  say 


124  MINE  GASES  AND  VENTILATION 

1  Ib.  of  dust  in  230  cu.  ft.  of  air.  In  one  instance  only,  ex- 
plosion occurred  in  23  grm.  per  cu.  m.  (0.023  oz.  per  cu.  ft.),  or 
1  Ib.  of  dust  in  about  700  cu.  ft.  of  air. 

It  is  quite  evident,  as  experiments  also  show,  that  condi- 
tions in  respect  to  the  purity,  humidity  and  particularly  the 
inflammability  of  the  dust  are  so  variable  that  the  question 
of  the  density  of  the  dust  cloud  has  only  an  experimental 
value.  The  size  of  the  workings,  as  determining  the  con- 
servation of  heat  and  pressure,  will  also  modify  the  results 
in  the  mine. 

Theoretically,  since  the  atomic  weights  of  carbon  and 
oxygen  are  12  and  16,  respectively,  1  Ib.  of  carbon  will  yield 

12+16       28 
— r~ —  =  —  =  2>i  Ib.  carbon  monoxide. 

I  -  iZ 

But,  carbon  monoxide  measures  13.5  cu.  ft.  per  Ib.,  at  normal 
temperature  and  pressure.  Hence,  2^  Ib.  of  this  gas  pro- 
duced by  1  Ib.  of  coal  dust  makes  2><j  X  13.5  =  31.5  cu.  ft. 
Then,  since  the  lower  inflammable  limit  is  reached  when  the 
mixture  of  gas  and  air  contains  8.4  per  cent,  of  the  gas,  inflam- 
mation might  be  expected  wThen  the  dust  present  was  1  Ib.  in 
31.5-7-  0.084  =  375  cu.  ft.  of  air.  Also,  the  lower  explosive 
limit  of  the  gas  occurring  when  1B.5  per  cent,  of  gas  is  present, 
explosion  might  be  expected  to  take  place  when  there  was 
1  Ib.  of  dust  in  31.5  +  0.165  =  190  cu.  ft.  of  air. 

Inflammability  of  Coal  Dust. — The  inflammation  of  a  dust 
cloud  in  mine  workings,  under  like  conditions,  depends  largely 
on  the  inflammable  nature  of  the  coal.  The  experiments  at 
different  testing  stations  have  demonstrated  that  the  volatile 
combustible  matter  contained  in  coal  is  a  fair  index  of  its 
susceptibility  to  inflammation  when  held  in  suspension  as 
fine  dust  in  the  air. 

Experiments  performed  with  anthracite  dust  seem  to  indicate 
that  the  fine  dust  of  that  coal  is  not  capable  of  propagating 
an  explosion  in  a  mine,  under  ordinary  mining  conditions. 
This  fact  points  significantly  to  the  conclusion  previously 
stated  that  the  volatile  combustible  matter  in  a  coal  is  an 
important  index  of  its  explosibility.  It  is  not  asserted  or 


EXPLOSIONS  IN  MINES  125 

claimed  that  anthracite  dust  cannot  be  exploded  under  favor- 
able conditions.  However,  the  conditions  that  would  cause 
anthracite  dust  floating  in  the  air  to  explode  are  not  liable 
to  occur  in  ordinary  mining  practice. 

Influence  of  Shale  or  Stone  Dust. — Shale  or  other  soft  rock 
of  the  coal  formations  have  been  ground  to  a  fine  powder 
for  use  in  mines  and,  in  this  form,  have  been  sprinkled  on  the 
roads  in  a  manner  to  form  stone -dust  zones,  or  distributed 
on  shelves  hung  across  and  overhead  in  the  entries  to  form 
so-called  stone-dust  "barriers." 

The  purpose  of  these  dust  zones  and  barriers  is  to  arrest 
the  progress  of  an  explosion  should  one  occur  in  the  mine. 
Their  use,  however,  has  not  been  attended  with  unvarying 
success,  which  is  due  in  part  to  the  different  conditions  of 
temperature,  humidity,  air  space  or  volume  of  mine  work- 
ings available  for  expansion,  inflammability  of  the  gas-  and 
dust-laden  air  and  the  initial  intensity  of  the  explosion;  also, 
in  part  to  the  limited  extent  or  adequacy  of  the  dust  zone  or 
barrier  as  compared  with  the  strength  developed  by  the 
explosion. 

Notwithstanding  the  apparent  failure  of  these  means  for 
preventing  the  spread  of  an  explosion  in  a  mine  in  many  ob- 
served instances,  there  is  no  question  but  that  finely  pow- 
dered shale  or  stone  dust  blown  into  the  path  of  an  explosive 
wave  by  the  pioneering  impulse,  or  suspended  in  the  air  with 
the  inflammable  coal  dust  has  a  most  decided  effect  and  re- 
duces explosive  conditions. 

The  action  of  incombustible  dust,  suspended  in  an  other- 
wise explosive  atmosphere,  to  allay  the  explosiveness  of  the 
mixture  or  reduce  the  violence  of  the  blast  should  ignition 
and  explosion  occur,  is  wholly  physical.  The  incombustible 
particles  disseminated  through  a  dust-laden  atmosphere  sepa- 
rate more  widely  the  inflammable  particles  of  coal  dust  and 
dilute  the  air  necessary  for  combustion.  In  other  words,  the 
percentage  of  inflammable  matter  in  the  mixture  is  reduced 
and  the  liability  to  inflame  diminished  in  the  same  proportion. 

Also,  by  its  absorption  of  heat,  the  incombustible  matter 
lessens  the  heat  available  for  ignition  and  decreases  the  heat 


126  MINE  GASES  AND  VENTILATION 

energy  developed  when  ignition  has  taken  place.  The  action 
is  entirely  similar  to  that  of  the  inert  nitrogen  of  air  depleted 
of  its  oxygen,  or  to  the  extinctive  effect  of  carbon  dioxide 
when  present  in  firedamp  mixtures,  both  of  which  conditions 
act  to  diminish  the  explosibility  of  gaseous  mixtures. 

MINE  EXPLOSION 

Development  of  a  Mine  Explosion. — Explosion  does  not  nec- 
essarily follow  the  ignition  of  gas  in  mine  entries  and  work- 
ings. The  firedamp  mixture  must,  of  course,  be  within  the 
explosive  range,  as  determined  by  the  conditions  in  that 
portion  of  the  mine.  But  even  then  a  mine  explosion  will 
only  take  place  when  the  conservation  of  heat  is  sufficient  to 
render  the  explosive  action  self-supporting.  Otherwise,  a 
local  explosion  of  gas  or  dust  will  expend  its  energy  within 
a  limited  area  and  the  disturbance  will  not  be  propagated 
throughout  the  mine. 

The  ignition  of  an  inflammable  mixture  of  gas  or  dust  in 
the  mine  air  may  produce  a  considerable  body  of  flame  that, 
within  the  narrow  confines  of  the  mine,  may  gather  force 
and  generate  sufficient  heat  to  cause  an  explosion.  Experi- 
ment has  shown  that  an  explosive  mixture  of  gas  and  air 
placed  in  a  tube  and  ignited  at  one  end  will  burn  quietly  at 
first,  then  flutter  or  vibrate  with  increasing  energy  as  the 
combustion  penetrates  deeper  in  the  tube,  the  contending 
forces  being  the  entering  air  and  the  escaping  products  of  the 
combustion.  This  action,  however,  quickly  develops  sufficient 
energy  to  produce  an  explosion,  which  darts  through  the 
entire  length  of  the  tube. 

This  experiment  illustrates  more  or  less  closely  the  devel- 
opment of  an  explosion  in  a  mine  entry  or  chamber.  Inves- 
tigation has  shown  that  the  explosion  gathers  force  and 
probably  develops  characteristic  energy  within  a  few  yards 
of  its  origin  or  the  point  where  the  ignition  of  the  gas  took 
place.  This  may  vary  from  10  to  30  yd.  or  more,  depending 
on  many  conditions — chiefly  the  size  or  volume  of  air  space 
available  for  the  expansion  of  the  gases  of  the  explosion,  the 


EXPLOSIONS  IN  MINES  127 

intensity  of  the  igniting  flame  and  inflammability  of  the 
mixture. 

All  of  these  factors  determine  severally  the  initiation  as 
well  as  the  character  of  the  explosion  and  its  limitations  in 
the  mine  workings.  . 

Causes  of  Mine  Explosions. — The  causes  of  mine  explosions 
may  be  generally  stated  as  the  ignition  of  gas  or  dust  by  one 
of  the  following  causes: 

1.  By  the  use  of  open  lights  or  defective  safety  lamps  in 
mines  where  the  air  current  is  charged  with  gas  or  dust,  or 
where  gas  has  accumulated  in  void  or  abandoned  places  in 
sufficient  quantities  to  be  dangerous. 

2.  By  the  use  of  mixed  lights  in  mines  generating  gas. 

3.  By  the  inexperienced  or  careless  use  of  a  safety  lamp, 
or  by  fooling  or  tampering  with  the  lamp,  or  exposing  it  to 
gas  too  long  or  to  a  strong  gas  blower  or  strong  current  or 
blast  of  air,  or  carrying  too  high  a  flame. 

4.  By  the  use  of  a  dirty  lamp  or  one  that  has  been  im- 
properly assembled  or  injured  by  a  fall  or  other  accidental 
cause. 

5.  By  the  explosion  of  powder  in  blasting  or  the  accidental 
explosion  of  a  keg  of  powder,  or  the  flame  of  a  blownout  shot 
or  a  windy  shot. 

6.  By  the  use  of  matches  or  other  means  of  lighting. 

7.  By  the  sparking  of  electric  wires,  switches  or  brushes, 
or  the  blowing  out  of  an  electric  fuse,  or  the  breaking  of  an 
incandescent  lamp. 

8.  By  the   spontaneous   ignition  of  oily   waste   carelessly 
thrown  aside,  or  of  fine  coal  or  slack  in  the  gob. 

9.  By  the  fall   of  certain  hard  roof  rock  striking  sparks, 
as  claimed  in  the  Bellevue  mine  explosion  (1910),  Alberta, 
Canada. 

10.  By  the  possible  generation  of  heat  due  to  concussion  of 
the  mine  air  in  contracted  workings  in  thin  seams. 

Mixed  Lights  in  Mines. — By  "mixed  lights"  is  meant  the 
use  of  open  lights  in  one  or  more  sections  of  a  mine  in  which 
gas  is  generated  in  other  portions  of  the  mine  in  sufficient 
quantity  to  require  safety  lamps  being  employed  therein. 


128  MINE  GASES  AND  VENTILATION 

The  expression  does  not  refer,  however,  to  the  use  of 
open  lights  by  drivers,  triprunners  or  motormen  whose 
duties  are  confined  to  the  main  intake  haulage  roads  and 
shaft  or  slope  bottom  of  a  mine  worked  on  safety  lamps, 
provided  there  are  lamp  stations  beyond  which  these  men 
may  not  pass. 

The  use  of  mixed  lights  is  a  dangerous  practice.  The 
danger  does  not  consist  wholly  in  a  man  carrying  an  open 
light  into  the  safety-lamp  section,  or  to  a  foreman  or  fire- 
boss  forgetting  that  he  has  an  open  light  on  his  head  while 
carrying  a  " safety"  at  his  side.  These  are  possibilities  that 
can  be  prevented  by  properly  safeguarding  the  entrances  to 
the  gaseous  section. 

The  real  danger  lies  in  a  heavy  fall  of  roof  occurring  in 
the  safety-lamp  section  and  driving  out  the  gas  into  other 
parts  of  the  mine  where  open  lights  are  in  use.  Or,  a  squeeze 
may  develop  in  any  part  of  the  mine  and  permit  the  gas  to 
find  its  way  without  warning  into  an  open-light  section  and 
cause  an  explosion. 

Electric  Mine  Lamps. — Any  installation  of  electricity  in  a 
mine  worked  on  safety  lamps  is  necessarily  accompanied  with 
more  or  less  danger.  Whether  the  installation  is  for  the  pur- 
posa  of  lighting,  hauling,  coal  cutting  or  drilling,  pumping  or 
ventilation,  it  should  be  made  by  a  competent  electrician. 
The  entire  system  of  wiring  should  be  closely  inspected  at 
frequent  intervals  and  tested  to  insure  freedom  from  short- 
circuiting  or  grounding  of  the  current,  which  are  not  only 
wasteful  of  power,  but  may  start  combustion  and  result  in  an 
explosion  of  gas. 

The  use  of  incandescent  lamps  in  mines  has  become  so  com- 
mon that  the  Bureau  of  Mines  has  made  a  careful  investiga- 
tion to  determine  their  safety.  Their  experiments  show  that 
ignition  of  gas  may  follow  the  breaking  of  the  glass  bulb  of 
a  lamp  in  an  explosive  mixture.  The  experiments  also  seem 
to  indicate  that  the  liability  of  ignition  increases  with  the 
cross-section  of  the  filament  of  the  lamp.  In  the  breaking  of 
an  incandescent  lamp  two  conditions  may  arise  that  materially 
affect  the  possibility  of  the  ignition  of  the  gas.  The  same 


EXTLOHIONS  IN  MINES  129 

blow  that  breaks  the  bulb  may  or  may  not  break  the  filament. 
The  result  in  either  case  may  be  briefly  explained  as  follows : 

1.  If   the  filament  is  broken  and  its  parts  do  not  short- 
circuit  the  current  ignition  of  the  gas  is  not  likely  to  occur. 
If  the  broken  parts,  however,  fall  across  each  other  in  such 
manner  as  to  again  close  the  circuit  their  burning  out  in  the 
air  will  generally  ignite  any  gas  present. 

2.  If  the  filament  remains  intact  when  the  bulb  is  broken 
it  will  burn  out  more  or  less  rapidly,  according  to  the  manner 
of  fracture  and  consequent  inrush  of  air  and  gas.     A  small 
hole  due  to  the  breaking  of  the  tip  may  admit  the  air  so  slowly 
that  the   gas   is   consumed   without  explosive   violence.     In 
that  case  there  may  occur  a  slight  explosion  within  the  bulb, 
which  is  not  broken  but  only  pierced.     This  feeble  explosion, 
however,  may  not  be  communicated  to  the  outside  gas. 

Prevention  of  Mine  Explosions. — No  means  has  yet  been 
devised  that  will  insure  absolute  freedom  from  mine  explo- 
sions. But  the  tendency  to  explosion  and  the  frequency  of 
these  occurrences  can  and  has  been  greatly  reduced  by  study- 
ing their  causes  and  adopting  measures  to  remove  them. 

The  following  points  are  of  chief  importance: 

1.  Effective  mine  regulations  and  discipline. 

2.  Operation  in  accordance  with  the  state  mining  law. 

3.  Enforcing   by   suitable   penalties   all   mine  regulations. 

4.  Thorough  frequent  inspection  by  competent  men. 

5.  Education  and  training  of  all  men  employed  in  any 
capacity  in  the  mine,  in  respect  to  the  proper  performance  of 
their  duties,  the  dangers  to  which  they  are  exposed  and  the 
mining  law  and  mine  regulations  in  force. 

6.  Eternal   vigilance   of   mine   officials   and   a   regard   for 
safety  greater  than  the  desire  for  increasing  the  daily  output 
of  the  mine. 

7.  Cooperation  of  employers  and  employed  in  increasing 
the  safety  of  mine  work. 

8.  Cooperation  of  all  coal  companies  in  respect  to  mining 
requirements. 

Aside  from  the  above  general  outline  there  is  the  necessity 
for  each  company  to  study  carefully  the  conditions  existing 


130  MINE  GASES  AND  VENTILATION 

in  its  own  mines,  and  to  adopt  a  system  of  inspection  and 
methods  of  ventilating  the  mine  and  mining  and  hauling  the 
coal  that  will  produce  the  best  results  and  insure  the  greatest 
freedom  from  accumulations  of  gas  and  dust  on  the  roads  and 
in  the  workings.  Immunity  from  explosion  can  only  be  se- 
cured by  removing  the  cause. 


SECTION  V 
MINE  RESCUE  WORK  AND  APPLIANCES 

PRELIMINARY,  ENTERING  A  MINE  AFTER  EXPLOSION,  FIRST- 
AID  SUGGESTIONS — BREATHING  APPARATUS,  PRINCIPLE, 
ACTION  AND  REQUIREMENTS  IN  RESPIRATION,  DEVELOP- 
MENT, DESIGN  AND  TESTING  OF  BREATHING  APPARATUS — 
TYPES  OF  BREATHING  APPARATUS,  DRAEGER,  FLEUSS 
PROTO,  GIBBS,  PAUL — BUREAU  OF  MINES,  PERMISSIBLE 
BREATHING  APPARATUS — SPECIFICATIONS  BY  THE  BU- 
REAU OF  MINES — FIRST-AID  WORK. 

PRELIMINARY 

Entering  a  Mine  after  an  Explosion. — Prompt  action  and 
intelligent  and  effective  measures  are  necessary  for  the  rescue 
of  any  possible  survivors  of  a  mine  explosion.  The  nature 
of  the  work  and  the  great  risk  incurred  in  its  undertaking 
demand  that  it  shall  be  performed  by  the  most  experienced 
of  the  volunteers,  of  whom  there  is  never  any  lack. 

Immediately  after  an  explosion  in  a  mine,  the  following 
procedure  is  important: 

1.  Call  for  volunteers  and  from  them  choose  those  who 
are  more  experienced  and  familiar  with  the  mine   and    the 
work  to  be  performed. 

2.  At  the  same  time,  observe  the  mine  entrances  and  judge 
of  the  probable  effect  of  "the  explosion  in  the.  mine;  examine 
the  ventilating  apparatus  and  have  any  necessary  repairs 
made  at  once. 

3.  Collect  the  necessary  safety  lamps,  tools,  timber,  can- 
vas, brattice  boards,  nails,  etc.     Caged  canaries  or  mice  should 
also  be  provided,  and  two  or  more  sets  of  breathing  apparatus 
should  make  up  the  equipment. 

4.  Divide  the  rescuers  into  three  parties,  as  follows: 
(a)  Apparatus  men  to  explore  in  advance; 

131 


132  MINE  GASES  AND  VENTILATION 

(b)  Repair  gang  and  rescuers; 

(c)  Supply  gang  to  render  every  possible  assistance. 
Organize  each  party  under  a  competent  leader  who  shall 

be  in  absolute  control  while  underground. 

5.  Enter  the  mine  at  the  earliest  possible  moment — the 
apparatus  men  proceeding  first  and  keeping  from  100  to  200 
yd.  in  the  lead  of  the  others,  who  must  not  advance  ahead  of 
the  air. 

6.  Each  section  of  the  mine  should  be  explored  by%  the 
apparatus  men  to  discover  any  possible  fire  therein,  before 
restoring  the  circulation  in  that  section. 

As  quickly  as  any  survivors  are  found  they  must  be  promptly 
removed  to  fresh  air  and  the  proper  restoratives  applied. 
At  the  surface,  physicians  should  be  in  attendance  and  am- 
bulances provided  for  the  prompt  removal  of  those  brought 
out  of  the  mine. 

Suggestions  on  First-aid  to  Explosion  Victims. — Those 
trained  in  first-aid  work  are  the  ones  who  should  assume 
charge  and  have  absolute  control  of  the  care  of  any  survivors 
as  quickly  as  found,  until  the  arrival  of  a  physician.  The 
following  brief  suggestions  are  important: 

1.  Be  calm  and  quiet;  act  promptly  but  not  in  a  hurry; 
keep  cool  and  observe  closely  every  symptom  and  condition. 

2.  Remove  promptly  but  carefully  to  fresh  air. 

3.  Do  everything  possible  to  stop  bleeding. 

4.  Examine  for  broken  bones  before  moving  far. 

5.  Use  aromatic  spirits  of  ammonia  if  stimulant  is  needed. 

6.  If  overcome  by  gas,  give  artificial  respiration. 

7.  If  unconscious,  loosen  clothing,  warm  and  stimulate  by 
rubbing  the  limbs;  give  no  stimulant  if  face  is  flushed  and 
pulse  strong,  but  sprinkle  cold  water  on  face  and  chest.     If 
the  body  and  limbs  are  cold,  use  warm  applications;  keep  the 
patient  covered  with  blanket  or  other  coverings;  apply  smell- 
ing salts  or  spirits  of  ammonia  cautiously  to  the  nostrils. 

BREATHING  APPARATUS 

Principle  of  Breathing  Apparatus. — The  principle  of  all 
breathing  apparatus  is  that  the  wearer  breathes  the  same  ah* 


MINE  RESCUE  WORK  AND  APPLIANCES  133 

over  and  over  again,  the  carbon  dioxide  exhaled  in  the  breath 
being  absorbed  after  each  expiration  while,  at  the  same  time, 
the  requisite  amount  of  oxygen  is  restored,  thus  rendering  the 
expired  air  pure  and  fit  to  be  again  inhaled. 

Action  in  Respiration. — In  the  act  of  inhalation,  the  air 
enriched  with  oxygen  passes  from  the  breathing  bag  in  the 
bottom  of  the  cooler,  up  through  the  latter  and  is  drawn 
through  the  inhalation  valve  and  tube  into  the  lungs. 

In  exhalations,  the  air,  deprived  of  some  of  its  oxygen  and 
containing  from  J^  to  4  per  cent,  of  carbon  dioxide,  depending 
on  the  amount  of  the  exertion,  is  discharged  through  the  ex- 
halation tube  and  valve  into  the  exhalation  side  of  the  cooler 
where  it  meets  the  oxygen  supply,  as  previously  stated,  and 
passes  into  the  regenerator  where  it  is  to  give  up  its  carbon 
dioxide,  by  contact  with  the  absorbent  caustic  soda. 

Requirements  in  Respiration. — The  average  full  capacity  of 
the  lungs  of  an  adult  person  is  about  300  cu.  in.  This  volume, 
however,  is  never  utilized  in  the  act  of  breathing;  that  is  to 
say,  all  of  the  air  contained  in  the  lungs  is  never  exhaled  or  the 
lungs  would  collapse,  which  would  be  fatal.  There  is  a  certain 
volume  of  residual  air,  about  100  cu.  in.,  that  remains  in  the 
lungs  after  a  deep  expiration.  In  the  ordinary  act  of  breathing, 
the  average  person  expires  only  about  20  or  30  cu.  in.  of  air  at  a 
single  breath.  This  has  been  called  "  tidal  air."  In  the  per- 
formance of  work  or  when  undergoing  any  extra  exertion,  a 
larger  quantity  of  air  is  expelled  from  the  lungs  at  each  breath 
and  a  corresponding  quantity  again  inhaled. 

The  ordinary  rate  of  respiration  is  16  breaths  per  minute 
when  a  person  is  at  rest,  making  the  volume  inhaled,  from  300 
to  500  cu.  in.  per  min.  When  making  violent  exertion  in  the 
performance  of  work,  breathing  is  more  rapid  and  a  much 
larger  volume  of  air  is  respired.  This  quantity  will  vary  with 
the  person  and  the  exertion  made  or  the  work  performed. 
When  doing  strenuous  work  a  man  may  inhale  200  cu.  in.  of 
air  at  a  single  breath. 

Approximately,  the  volume  of  carbon  dioxide  exhaled  is 
equal  to  that  of  the  oxygen  breathed  into  the  lungs,  the  ratio 
of  carbon  dioxide  to  oxygen  being  slightly  less  when  the  person 


134 


MINE  GASES  AND  VENTILATION 


is  at  rest,  than  it  is  in  the  performance  of  work.  However,  for 
the  purposes  of  ordinary  estimate,  it  may  "be  assumed  that  a 
man,  at  rest,  will  inhale  from  25  to  30  cu.  in.  of  air  at  a  single 
breath  and  this  may  be  increased  to  150  or  possibly  200  cu.  in. 
when  making  violent  exertion.  Practically,  one-fifth  of  this 
volume  of  air  is  oxygen ;  but,  in  the  act  of  breathing,  only  one- 
third  or  one-half  of  this  oxygen  is  consumed. 

The  standard  supply  of  oxygen,  in  mine  breathing  apparatus, 
has  been  fixed,  therefore,  at  2  liters  per  min.  (122  cu.  in.). 
Compressed  to  120  atmospheres,  this  rate  of  supply  of  oxygen, 
for  a  2-hr,  period,  will  require  a  cylinder  capacity  of  2(122  X 
60)  -f-  120  =  122  cu.  in.  Again,  assuming  that  the  average 
amount  of  carbon  dioxide  produced  in  breathing  is  equal  to  the 
volume  of  oxygen  consumed,  it  appears  that  the  quantity  of 
the  former  gas  required  to  be  absorbed  by  the  caustic  soda  in 
the  regenerator,  in  a  2-hr,  period,  is  2(2  X  60)  =  240  liters, 
or  8.47  cu.  ft. 

The  following  table  gives  carefully  compiled  data  and  the 
results  of  actual  tests  regarding  the  oxygen  consumed,  carbon 
dioxide  produced,  quantity  of  air  breathed  and  number  of 
respirations  per  minute,  under  different  conditions  of  rest  and 
exertion.  These  data  were  compiled  by  James  M.  Stewart, 
Instructor  at  the  Brazeau  Rescue  Station,  Alberta,  Canada.* 

DATA  REGARDING  Am  RESPIRED  WHEN  WALKING  AND  AT  REST 


Condition  of  subject 

Oxygen 
consumed 
per  minute 
in  liters 

C02 
expired 
per  minute 
in  liters 

Air 
breathed 
per  minute 
in  liters 

Average 
volume 
of  each 
breath 

Number 
of  breaths 
per  minute 

At  rest  in  bed  .  .  . 

0   237 

0  197 

7.7 

0.457 

16.8 

At  rest,  standing  

0.328 

0.264 

10.4 

0.612 

17.1 

Walking,  2  mi.  per  hr. 

0.780 

0.662 

18.6 

1.270 

14.7 

Walking,  3  mi.  per  hr. 

1.065 

0.992 

24.8 

1.530 

16.2 

Walking,  4  mi.  per  hr. 

1.595 

1.395 

37.3 

2.060 

18.2 

Walking,  4*£  mi.  per 

hr  

2  005 

1.788 

46.5 

2  .  520 

18.5 

Walking,  5  mi.  per  hr. 

2.543 

2.386 

60.9 

3.140 

19.5 

*  Bulletin,  November,  1916,  Rocky  Mountain  Branch  of  the  Canadian 
Mining  Institute. 


-  MINE  RESCUE  WORK  AND  APPLIANCES  135 

It  is  evident  from  the  table  that  more  than  the  standard 
supply  of  oxygen  allowed  in  the  design  of  breathing  apparatus 
may  be  consumed  by  a  person  under  great  physical  exertion. 
Mr.  Stewart  suggests,  therefore,  that  it  is  of  the  utmost  im- 
portance that  the  captain  of  a  rescue  team  observe  carefully 
that  his  men  do  not  overexert  themselves  while  in  the  per- 
formance of  their  duties  in  the  mine.  He  also  suggests  that, 
in  the  use  of  the  nose-clip,  greater  comfort  and  security  is 
obtained  by  inserting  a  cotton-wool  plug  in  each  nostril, 
before  adjusting  the  clip. 

Development  of  Breathing  Apparatus. — The  development 
of  breathing  apparatus,  during  the  past  few  years,  since  the 
Government  took  up  the  work  of  improving  mining  conditions 
(1907)  has  been  rapid.  In  the  earlier  types  of  apparatus,  a 
helmet  was  employed  to  cover  the  head  and  oxygen  was 
supplied  through  rubber  tubes  that  connected  the  helmet  with 
a  gas  cylinder  or  bag  containing  the  gas.  Owing  to  the  dan- 
ger of  these  connecting  tubes  being  broken  in  the  rough  service 
to  which  they  are  subjected  in  the  mine,  the  first  attempt  to 
improve  the  apparatus  resulted  in  the  adoption  of  a  form  that 
was  self-contained,  so  as  to  eliminate,  as  far  as  practicable, 
the  tube  connections. 

Mining  practice  quickly  demonstrated  that  the  substitution 
of  a  simple  mouthpiece,  and  noseclip  to  close  the  nostrils,  gave 
better  service  underground  than  the  clumsy  helmet,  although 
the  latter  afforded  more  comfort  in  breathing  and  enabled 
the  wearer  to  talk  to  his  comrades  with  greater  facility 
than  when  the  mouthpiece  was  used  and  a  noseclip  closed 
the  nostrils.  However,  these  disadvantages  were  largely  out- 
weighed by  the  greater  facility  offered  for  work  by  this  form 
of  apparatus. 

Design  of  Breathing  Apparatus. — Breathing  apparatus  is 
designed  to  supply  the  wearer  with  a  perfectly  respirable  air 
independent  of  the  atmosphere  in  which  he  may  be  placed. 
The  design  of  the  apparatus  is  to  enable  the  wearer  to  work  in 
an  irrespirable  atmosphere  for  a  limited  period  of  two  hours. 
The  principal  features  of  the  device  consist  in  maintaining  a 
sufficient  supply  of  oxygen  to  replace  that  consumed  by  the 


136  MINE  GASES  AND  VENTILATION 

wearer  of  the  apparatus,  and  absorbing  the  carbon  dioxide  he 
exhales. 

Oxygen,  compressed  to  120  atmospheres,  is  contained  in  a 
strong  steel  cylinder.  The  quantity  is  sufficient  to  afford  a 
supply  of  2  liters  of  this  gas  (122  cu.  in.,  normal  temperature 
and  pressure)  per  minute.  A  pressure  of  120  atmospheres, 
at  sea  level,  corresponds  to  about  1800  Ib.  per  sq.  in.  A  re- 
ducing valve  is  employed  to  control  this  pressure  and  reduce  it 
to  the  normal  pressure  of  the  atmosphere,  for  breathing.  An 
air-tight  breathing  bag  filled  with  pure  air  and  equipped  with 
a  release  valve,  forms  part  of  the  apparatus  and  is  connected 
directly  with  the  oxygen  supply  cylinder  and  the  helmet  or 
mouthpiece. 

Another  important  feature  of  breathing  apparatus  is  the  re- 
generator, holding  a  supply  of  4  or  5  Ib.  of  caustic  soda  or 
caustic  potash.  This  minimum  weight  of  caustic  soda  (4  Ib.) 
will  absorb,  if  fully  utilized,  532  liters  of  carbon  dioxide  and  is 
ample  for  all  contingencies.  By  the  absorption  of  the  carbon 
dioxide,  the  caustic  soda  is  converted  into  sodium  carbonate 
and  some  water  is  produced  according  to  the  equation 

2NaOH  +  CO2  =  Na2CO3  +  H2O 

The  molecular  weight  of  the  caustic  soda  or  sodium  hydrox- 
ide is  2(23  +  16  +  1)  =  80,  while  the  molecular  weight  of  the 
carbon  dioxide  is  12  +  2  X  16  =  44.  The  ratio  of  the  weight 
of  carbon  dioxide  absorbed  to  that  of  the  caustic  used  is,  there- 
fore, 4^o  =  1MoJ  and  the  4  Ib.  of  caustic  soda,  if  completely 
utilized,  would  absorb  4(1^0)  =  2.2  Ib.,  or  18.78  cu.  ft.  of 
carbon  dioxide  (532  liters),  at  normal  temperature  and  pressure. 

In  the  absorption  of  carbon  dioxide,  however,  the  caustic 
soda  becomes  encrusted  with  the  sodium  carbonate  formed, 
which  prevents  or  at  least  impedes  the  action  of  absorption. 
The  shaking  of  the  regenerator  helps  to  break  up  this  crust 
and  restore  the  absorptive  power  of  the  caustic. 

Testing  Breathing  Apparatus. — All  breathing  apparatus 
should  be  regularly  tested  to  insure  its  perfect  condition. 
Especially  should  this  be  done  by  the  wearer  before  he  enters 
an  irrespirable  atmosphere.  The  apparatus  may  be  defective 


MINE  RESCUE  WORK  AND  APPLIANCES  137 

from  any  one  of  a  number  of  such  causes  as  negative  pressure ; 
leaks  in  joints,  tubes,  breathing  bag  or  other  container;  ob- 
structed valves  or  tubes,  imperfect  regeneration,  owing  to 
insufficient  absorption  of  carbon  dioxide  or  inadequate  supply 
of  oxygen;  etc 

Before  putting  on  the  apparatus,  the  wearer  should  examine 
and  test  its  various  parts  to  ascertain  that  it  is  tight,  the  valves 
and  tubes  free  from  obstruction  and  the  supply  of  oxygen  and 
caustic  soda  adequate.  Each  tube,  the  bag  and  the  assembled 
apparatus  should  be  tested  for  leaks,  by  means  of  the  pressure 
gage  and  observing  the  constant  water  level  in  the  U  tube 
kept  for  that  purpose.  The  old  habit  of  immersing  apparatus 
in  water  to  show  leakage  is  harmful. 

TYPES  OF  BREATHING  APPARATUS 

The  principal  types  of  breathing  apparatus  now  in  use  in 
this  country  are  the  Draeger  breathing  apparatus,  the  Fleuss 
Proto  apparatus,  the  Paul  type  of  apparatus  and  the  more 
recent  and  highly  improved  Gibbs  apparatus,  which  combines 
all  of  the  best  features  of  other  types  and  many  improvements. 

Draeger  Breathing  Apparatus. — There  are  two  general  types 
of  this  apparatus,  one  employing  the  helmet  and  the  other  the 
noseclip  and  mouthpiece.  These  two  types  are  shown  in 
Fig.  14  together  with  side  and  rear  views  of  the  apparatus  as 
worn  by  the  rescuer.  Owing  to  its  bulkiness  the  helmet  type 
is  not  so  well  adapted  to  mine  work  as  that  equipped  with  the 
noseclip  and  mouthpiece. 

Since  its  introduction  in  1903  the  Draeger  apparatus  has 
undergone  various  marked  improvements  and  is  at  present 
one  of  the  standard  types  of  rescue  appliances  in, use.  The 
canvas  breathing  bags,  one  for  inhalation  and  the  other  for 
exhalation,  are  rubber-lined.  The  oxygen  cylinder  is  sup- 
plied with  a  perfected  high-pressure  valve  that  enables  the 
wearer  to  shut  off  the  pressure  at  any  moment  desired,  by  a 
simple  thumb  pressure.  These  together  with  the  safety 
locked  couplings  securing-  all  tube  connections,  and  the  time 
recorder  and  pressure  gage,  always  ready  for  inspection  by 
the  wearer,  insure  both  safety  and  comfort. 


138 


MINE  GASES  AND  VENTILATION 


MINE  RESCUE  WORK  AND  APPLIANCES 


139 


Essential  Parts. — The  diagram,  Fig.  15,  shows  the  arrange- 
ment of  the  several  parts  of  the  apparatus  for  the  purpose  of 
making  clear  their  relation  and  the  circulation  of  the  system. 
The  diagram  shows  the  helmet  H,  the  expiration  valve  V2, 
the  exhalation  bagL2,  that  receives  the  exhaled  air,  the  regen- 
erator R,  the  cooler  K,  the  aspiration  pipe  C,  the  inhalation 
bag  LI,  holding  the  purified  air  and  the  inspiration  valve  V\. 
The  oxygen  cylinder  and  pressure  gage  also  appear,  the  former 
has  withstood  an  official  test  of  225  atmospheres  and  is  com- 
monly charged  to  a  pressure  of  120  atmospheres. 


R 


FIG.  15. 

Capacity  of  the  Apparatus. — This  apparatus  will  purify 
about  3000  liters  (105  cu.  ft.)  of  air  per  hour,  besides  supplying 
120  liters  (4.2  cu.  ft.)  of  oxygen, and  absorb  50  liters  (1%  cu.ft.) 
of  carbon  dioxide.  This  is  claimed  to  enable  the  wearer  of  the 
apparatus  to  perform  260,000  ft.-lb.  of  work.  While  an  un- 
trained man  will  generally  do  less  than  this,  the  work  done 
in  one  instance  amounted  to  398,000  ft.-lb. 

Fleuss  Proto  Apparatus. — This  apparatus  is  designed  to 
supply  the  user  with  a  perfectly  respirable  air,  entirely  inde- 
pendent of  any  communication  with  the  outside  atmosphere 


140 


MINE  GASES  AND  VENTILATION 


for  at  least  two  hours  at  a  time.  It  has  been  designed  to  with- 
stand the  severe  conditions  to  which  it  must  be  subjected  in 
mining  use  and  insure  the  safety  of  the  wearer  while  engaged 
in  the  dangerous  work  of  rescuing  men  from  mine  workings 
filled  with  poisonous  or  irrespirable  gases. 


FIG.  16. 

Front  and  rear  views  of  the  apparatus  are  shown  in  the 
Fig.  16,  in  the  position  in  which  it  is  worn,  the  large,  double- 
compartment  breathing  bag  being  in  front  and  the  oxygen 
cylinder  in  the  rear  of  the  wearer.  A  diagrammatic  view  is 
shown  on  the  opposite  page  (Fig.  17)  explaining  the  various 
parts  of  the  apparatus. 

Essential  Parts. — The  principal  features  are  the  oxye-en 
cylinder  B;  the  reducing  valve  C;  the  breathing  bag  D  with 


MINE  RESCUE  WORK  AND  APPLIANCES. 


141 


inhaling  and  exhaling  divisions;  inspiratory  and  expiratory 
valves  T  and  8;  mouthpiece  and  noscclip  R  and  Y. 

The  wearer  exhales  through  valve  *S,  the  air  passing  down 
one  side  of  the  partition  of  the  breathing  bag  and  through  the 
caustic  soda,  which  absorbs  the  carbon  dioxide,  and  thence  up 

OXYGEN 
CYLINDER 


PRESSURE  CAUCE 


MAIN  VALVE 


EXHALING  VALV 
RELIEF  VAL 

SALIVA  TRAP 


END   SECTION 
SHEWING  CAUSTIC 
SODA  SPACES 


BREATHING  BAC 
WITH  INHALING 
AND  EXHALING 
COMPARTMENTS 


REDUCING  VALVE 
BY- PASS 


SKULL  CAP 

SMOKE  COCCUS 
NOSE  CLIP 
MOUTH  PIECE 


>      JNHALINC  VALVE 


FIG.  17. 


the  other  side  of  the  partition  to  valve  T  to  be  again  inhaled, 
after  mixing  with  fresh  oxygen,  which  is  being  constantly  de- 
livered at  the  rate  of  two  liters  per  minute  from  the  oxygen 
cylinder  through  the  reducing  valve  C.  Connected  to  a 
flexible  tube  IF  is  a  pressure  gage  P  indicating  the  quantity 
of  oxygen  in  the  cylinders  and  the  duration  of  supply.  An 


142  MINE  GASES  AND  VENTILATION 

emergency  by-pass  7  is  for  use  in  case  the  reducing  valve  fails ; 
it  enables  the  wearer  to  fill  his  breathing  bag  direct  from  the 
oxygen  cylinders.  A  saliva  trap  Z  prevents  the  saliva  from 
entering  the  breathing  bag. 

The  steel  cylinder  contains  about  10  cu.  ft.  of  oxygen,  com- 
pressed to  120  atmospheres,  which  gives  a  two-hours'  supply 
when  the  reducing  valve  is  passing  two  liters  per  minute. 
The  cylinder  can  be  charged  to  150  atmospheres  if  desired, 
which  will  give  a  2^  hour-supply. 

A  reducing  valve  C  is  fitted  to  the  bottle  nipple  and  is  so 
adjusted  as  to  pass  a  regular  supply  of  from  2  to  2J<£  liters  of 
oxygen  per  minute,  no  matter  what  the  pressure  may  be  in  the 
cylinder.  This  valve  can  be  readily  adjusted  to  deliver  any 
flow  from  one  to  three  liters  per  minute,  as  desired.  The 
valve  is  fitted  with  a  by-pass,  having  a  small  wheel  valve  I 
so  that  should  it  from  any  cause  fail  to  act  properly  the 
wearer  of  the  apparatus  can  supply  himself  with  what  oxygen 
he  requires  direct  from  the  cylinder  by  turning  the  small 
valve.  Also,  by  the  same  means,  the  automatic  supply  of  two 
liters  per  minute  can  be  increased  at  any  time  by  the  wearer  if 
desirable.  When  working  in  an  excessively  hot  atmosphere 
it  is  possible  to  cool  the  hot  air  by  exhausting  all  the  air  from 
the  bag  through  the  relief  valve  K,  and  then  filling  the  bag 
with  pure,  cool  oxygen  from  the  cylinder,  by  means  of  this 
by-pass. 

The  reducing  valve  delivers  the  oxygen  through  the  flexible 
tube  F  to  the  breathing  bag  D,  carried  on  the  wearer's  chest. 
Another  connection  at  V ,  made  through  a  flexible  high  pres- 
sure tube  W  with  a  pressure  gage  P,  carried  in  a  pocket  of  the 
canvas  cover,  enables  the  wearer  to  ascertain  the  available 
supply  and  duration  of  oxygen.  Each  division  of  the  pressure 
gage  indicates  10  atmospheres  of  pressure,  or  10  minutes  of 
time,  assuming  the  valve  to  be  passing  two  liters  per  minute. 
The  connection  V  is  also  fitted  with  a  small  valve,  to  enable 
the  wearer  to  shut  off  the  oxygen  should  the  gage  or  its  flexible 
tube  become  damaged. 

The  breathing  bag  D  is  of  strong  vulcanized  India  rubber 
and  contained  in  an  outer  strong  canvas  bag.  The  rubber 


MINE  RESCUE  WORK  AND  APPLIANCES  143 

bag  has  two  compartments,  connected,  however,  at  the  bottom 
of  the  bag.  The  bag  is  fitted  at  the  upper  left-hand  corner 
with  a  saliva  trap  Z  and  relief  valve  K  to  allow  the  escape  of 
any  excess  oxygen  that  might  be  delivered  by  the  reducing 
valve.  At  the  upper  right-hand  corner  is  a  small  connection 
N  for  the  oxygen  supply  from  the  cylinder.  The  mouth  of  the 
bag  is  closed  with  metal  clamps  and  wing  nuts  0. 

The  mouthpiece  is  of  soft  vulcanized  India  rubber,  fitted  to 
a  German  silver  connection  R  and  shaped  to  fit  comfortably 
between  the  lips  and  the  gums.  To  the  connecting  piece  R 
are  also  fitted  strong  flexible  corrugated  tubes  XX,  sometimes 
called  "  bellows  tubes, "  to  the  opposite  ends  of  which  are  fitted 
the  exhaling  and  inhaling  valves  S  and  T,  respectively.  These 
valves  are  of  mica  and  extremely  sensitive.  They  are  screwed 
into  their  respective  connections  L  and  M .  The  noseclip  Y 
is  made  to  fit  any  nose  comfortably.  The  skull  cap  has  a 
back  apron  to  which  the  mouthpiece  can  be  securely  buckled, 
which  supports  it  comfortably. 

One  feature  of  the  Fleuss  Proto  apparatus  is  the  fact  that 
the  caustic  soda  is  held  in  a  bag  instead  of  a  rigid  container 
and  the  movements  of  the  wearer  when  walking  or  at  work 
automatically  rubs  off  the  carbonated  surface  of  the  soda,  and 
constantly  exposes  a  fresh  surface  for  the  absorption  of  car- 
bon dioxide.  The  bag  is  easily  emptied  after  use,  and  a  fresh 
supply  of  soda  added  at  once,  thus  making  the  apparatus  ready 
for  use  again  in  two  or  three  minutes.  The  bag  is  so  con- 
structed that  external  pressure  on  it  does  not  impede  the 
wearer's  breathing.  In  fact,  a  man  may  lie  flat  upon  the  bag 
and  still  be  able  to  breathe  freely. 

Gibbs  Breathing  Apparatus. — This  form  of  apparatus  was 
developed  by  W.  E.  Gibbs,  of  the  Federal  Bureau  of  Mines, 
who  sought  to  improve  on  the  older  types  of  English  makes  of 
breathing  apparatus  in  mining  use. 

The  general  requirements  sought  to  be  fulfilled  in  this  de- 
sign were:  (1)  Automatic  control  of  oxygen  supply  in  rest  or 
exertion.  (2)  Adequate  absorption  of  carbon  dioxide.  (3) 
Freedom  of  respiration  under  constant  positive  pressure. 
(4)  Avoiding  collapse  of  breathing  bag  from  any  cause.  (5) 


144 


MINE  GASES  AND  VENTILATION 


Efficient  heat  radiation  and  cooling  to  avoid  high  temperature. 
(6)  Simplicity,  durability  and  strength  and  tight  joints  in 
every  part. 

The  position  of  the  apparatus  when  in  use  is  shown  by  the 
side  and  rear  views  in  the  Fig.  18.  For  the  better  protection 
of  the  parts  from  injury,  in  the  mine,  a  cover  is  provided  as  a 


FIG.  18. 

shield.  The  general  arrangement  of  the  pai*ts  is  shown  by  the 
Fig.  19  in  which  the  several  elements  are  numbered  to  cor- 
respond to  their  description  in  the  text. 

Circulation  in  the  Apparatus. — Oxygen  from  the  bottle  (1) 
in  which  it  is  compressed  to  135  atmospheres,  passes  through 
the  closing  valve  (2)  to  the  reducing  valve  (3) ;  thence,  under 
normal  pressure,  by  rubber  tube  connection,  it  passes  through 


MTNE  RESCUE  WORK  AND  APPLIANCES 


145 


a  metal  tube  surrounded  by  a  cooler;  through  an  admission 
valve  into  another  metal  tube  inclosed  in  cooler,  being  then 
discharged  into  the  exhalation  side  of  the  cooler  where  it  meets 
the  exhaled  air  and  passes  downward  with  it  into  the  regenera- 
tor; then  upward  into  the  inhalation  side  of  the  cooler,  where 


FIG.  19. 

it  enters  the  breathing  bag  in  the  cooler.  From  the  breathing 
bag  the  air  passes  through  an  inhalation  valve  and  enters  the 
lungs,  from  which  it  is  discharged  through  the  exhalation  tube 
into  the  exhalation  side  of  the  cooler. 

Testing  Gibbs  Apparatus. — The  following  series  of  tests  of 
the    Gibbs    breathing   apparatus   are   recommended   by   its 
manufacturers : 
10 


146  MINE  GASES  AND  VENTILATION 

1.  Oxygen   bottle   should   be    charged  to    135   atmospheres.        The 
oxygen  cylinder  being  tested  under  water  for  leaks,  with  main  valve  both 
open  and  closed.     The  cylinder  is  first  tested  with  valve  closed,  then  cap 
is  placed  on  cylinder  and  tested  with  valve  open.     Connect  oxygen  bottle 
to  reducing  valve,  using  wrench  in  order  to  make  tight  connections. 

2.  Examine  seals  of  regenerators  in  order  to  see  that  they  are  not 
broken.     Connect  regenerator  to  cooler,  being  sure  that  gaskets  are  in 
place  between  the  connections.     Screw  down  screws  by  hand  and  tighten 
with  screw  driver. 

3.  Lift  breathing  bag  from  bumper  on  admission  valve,  then  turn 
on  main  oxygen  valve. 

Observe  mica  inhalation  valve — if  admission  valve  leaks  the  mica 
inhalation  valve  will  raise  and  let  oxygen  escape. 

Turn  pressure  tube  valve  on  and  observe  the  number  of  atmospheres 
indicated  by  the  pressure  gage.  Pressure  gage  valve  should  always 
be  left  open.  Squeeze  bellows  of  reducing  valve  in  order  to  open  seat 
over  orifice;  this  approximately  increases  the  pressure  to  five  pounds  in 
rubber  tube  and  metal  tube.  Safety  valve  will  whistle  at  the  above  pres- 
sure if  working  properly.  Try  all  connections  from  oxygen  bottle  to 
cooler  for  leaks  by  using  brush  and  soap  suds.  Turn  off  main  oxygen 
valve. 

4.  Blow  into  exhalation  valve  and  observe  air  returning  by  way  of 
inhalation  valve,  showing  circulation  of  air  through  exhalation  side  of 
cooler,  regenerator,  inhalation  side  of  cooler,  and  breathing  bag.     Next, 
close  inhalation  valve  either  by  cupping  hand  over  valve  or  by  special 
connection,  then  blow  into  exhalation  valve  until  bag  is  fully  inflated. 
Exhalation  valve  seat  and  mica  should  make  an  air  tight  connection, 
keeping  bag  fully  inflated.     Test  all  connections  for  leaks,  using  brush 
and  soap  suds. 

5.  Connect  mouthpiece  to  cooler,  seeing  that  gaskets  are  in  place. 
Inflate  breathing  bag  and  test  mouthpiece  connections  for  leaks,  using 
brush  and  soap  suds.     Try  release  valve  and  saliva  pumps  for  leaks. 

6.  After    apparatus   has  been  tested  and  adjusted  to  wearer,  before 
adjusting  noseelip,  it  is  essential  that  the  wearer  turn  on  main  oxygen 
valve,  inhale  from  apparatus,  exhale  into  open  air  several  times  before 
readjusting  the  clip.     In  this  way  a  high  percentage  of  oxygen  and  a  low 
percentage  of  nitrogen  will  be  contained  in  breathing  apparatus.     While 
inhaling  from  the  apparatus  the  wearer  will  observe  whether  the  whole 
apparatus  is  functioning  properly.     After  noseelip  is  adjusted,  the  wearer 
is  ready  for  a  preliminary  test  in  room  filled  with  fumes.     After  remain- 
ing in  room  for  five  (5)  minutes  and  no  leaks  being  observed,  the  wearer 
can  feel  assured  that  his  apparatus  is  in  good  working  condition  for  doing 
work  in  poisonous  gases  and  irrespirable  air. 

7.  Under  no.  circumstances  should  grease  or  oil  be  used  on  apparatus 
parts. 


MINE  RESCUE  WORK  AND  APPLIANCES  147 

The  Paul  Breathing  Apparatus. — This  type  of  apparatus 
was  designed  by  James  W.  Paul,  long  in  charge  of  the  mine- 
rescue  work,  as  engineer  of  the  Federal  Bureau  of  Mines,  at 
Pittsburgh,  Penn.  The  apparatus  is  manufactured  by  the 
old  Draeger  Company,  now  known  as  the  American  Atmos 
Corporation,  Mr.  Paul  having  disposed  of  his  right  and  title 
in  the  apparatus  to  that  company. 

One  of  the  highly  essential  improvements  of  the  Paul 
apparatus,  which  is  modeled  chiefly  after  the  Gibbs,  is  the 
combination  of  the  self-adjusting  oxygen-feed  valve  with  a 
low-pressure  oxygen-control  valve,  at  the  intake  of  the  cir- 
culatory system.  This  device  regulates  the  supply  of  oxygen 
and  proportions  it  to  the  rate  of  consumption,  which  varies 
with  the  work  performed  by  the  wearer.  Also,  a  pressure 
slightly  in  excess  of  1  cm.  of  water  column  is  automatically 
maintained  in  the  system  and  minimizes  the  liability  of 
an  outside  poisonous  atmosphere  penetrating  within  the 
apparatus. 

BUREAU  OF  MINES 

The  Federal  Bureau  of  Mines  recommends  that  the  circu- 
lation in  breathing  apparatus  be  under  positive  pressure 
throughout  and  that  the  apparatus  be  equipped  with  mouth- 
piece and  noseclip  and  provided  with  a  by-pass  valve.  The 
helmet,  for  mining  use,  is  objectionable  and  dangerous,  not 
only  because  of  the  difficulty  of  obtaining  a  perfectly  air- 
tight joint  around  the  face,  but  also  because  it  is  easily 
dislodged  and  greatly  cuts  down  the  range  of  vision.  Also, 
the  large  dead-air  space  in  the  helmet  permits  an  excessive 
accumulation  of  carbon  dioxide. 

The  injector  used  in  some  types  of  breathing  apparatus  is 
complicated  and  liable  to  be  out  of  order  when  needed.  Any 
slight  particle  is  sufficient  to  choke  the  orifice  and  cut  off  the 
supply  of  oxygen.  The  use  of  the  injector  also  involves  a 
negative  pressure,  which  would  cause  an  inflow  of  the  sur- 
rounding atmosphere  into  the  apparatus  should  there  be  any 
leak  in  the  joints  or  tube  connections. 


148  MINE  GASES  AND  VENTILA  TION 

Permissible  Breathing  Apparatus. — Owing  to  the  grave 
importance  of  securing  safe  types  of  mining  appliances  manu- 
factured in  this  country,  an  act  of  Congress  (37  Stat.,  681), 
approved  Feb.  25,  1913,  authorized  the  director  of  the  Bureau 
of  Mines  to  prescribe  rules  and  regulations  for  testing  such 
appliances  as  may  be  submitted  to  the  bureau  for  that  purpose. 

Acting  under  this  authority  the  Federal  Bureau  of  Mines 
has  prepared  and  published,  Mar.  5,  1919,  "Schedule  13," 
defining  the  requirements  necessary  to  establish  a  list  of  so- 
called  " Permissible"  self-contained,  mine-rescue,  breathing 
apparatus.  Following  are  the  more  important  specifications 
contained  in  that  schedule. 


Definition. — The  Bureau  of  Mines  considers  a  self-contained  mine- 
rescue  breathing  apparatus  to  be  permissible  for  use  in  irrespirable  and 
poisonous  gases  if  all  the  details  of  construction  and  materials  are  the 
same  in  all  respects  as  those  of  the  self-contained  mine-rescue  breathing 
apparatus  that  met  the  requirements  and  passed  the  tests  for  safety,  prac- 
ticability and  efficiency  made  by  the  bureau  and  hereinafter  described. 

Conditions  of  Testing. — The  conditions  under  which  the  Bureau  of 
Mines  will  examine  and  test  self-contained  mine-rescue  breathing  appa- 
ratus to  establish  their  permissibility  are  as  follows: 

1.  The  examination,  inspection,  and  test  shall  be  made  at  the  experi- 
ment station  of  the  Bureau  of  Mines  at  Pittsburgh,  Pa. 

2.  Applications  for  inspection,  examination,  and  test  shall  be  made 
to  the  Director,  Bureau  of  Mines,  Washington,  D.  C.,  and  shall  be 
accompanied  by  a  complete  written  description  of  the  self-contained 
mine-rescue  breathing  apparatus  including  the  regenerator,  and  a  set 
of  drawings  showing  full  details  of  construction  of  both  the  regenerator 
and  the  apparatus. 

3.  The  applicant  submitting  the  self-contained  mine-rescue  breathing 
apparatus  for  inspection,  examination,  and  test  will  be  required  to  furnish 
the  apparatus  in  duplicate,  which  shall  be  sent  prepaid  to  the  mine- 
safety  engineer,  Bureau  of  Mines,  4800  Forbes  Street,  Pittsburgh,  Penn. 
In  the  event  of  the  apparatus  successfully  passing  all  of  the  Bureau  of 
Mines  tests  and  requirements  hereinafter  specified,  one  set  will  be  re- 
tained by  the  Bureau  of  Mines  as  a  laboratory  exhibit  and  the  other  set 
will  be  returned  to  the  owner.     In  the  event  that  an  apparatus  does  not 
pass  all  of  the  bureau's  tests  or  requirements,  both  sets  will  be  returned 
to  the  owner. 

4.  Each  self-contained  mine-rescue  breathing  apparatus  shall  have 
marked  on  it  in  a  distinct  manner  the  name  of  the  manufacturer  and  the 
name,  letter,  or  number  by  which  the  type  is  designated  for  trade  pur- 


MINE  RESCUE  WORK  AND  APPLIANCES  149 

poses,  and  a  written  statement  shall  be  made  whether  or  not  the  appa- 
ratus is  ready  to  be  marketed. 

5.  The  applicant  will  supply  the  regenerators  or  regenerating  material 
for  the  test.     For  tests  of  self-contained  mine-rescue,  oxygen  breathing 
apparatus  dependent  on  a  supply  of  compressed  gaseous  oxygen,  the 
oxygen  will  be  supplied  by  the  Bureau  of  Mines  and  will  be  of  the  purity 
specified  by  the  bureau  in  contracts  for  the  supply  of  its  safety  cars  and 
stations;  namely,  98  or  more  per  cent,  oxygen  and  not  more  than  0.2  of 
1  per  cent,  hydrogen;  other  impurity  to  consist  of  nitrogen  only. 

6.  Upon  receipt  of  the  self-contained  mine-rescue  breathing  apparatus 
for  which  application  has  been  made  for  examination,  inspection,  or 
test,  the  mine-safety  engineer  in  charge  of  breathing-apparatus  testing 
will  advise  the  applicant  whether  additional  spare  parts  are  deemed 
necessary  to  facilitate  a  proper  test  of  the  apparatus,  and  the  applicant 
will  be  required  to  furnish  such  parts  as  may  be  necessary. 

7.  No  self-contained  mine-rescue  breathing  apparatus  will  be  tested 
unless  the  type  submitted  is  in  the  complete  form  in  which  it  is  to  be 
placed  on  the  market. 

8.  Only  the  Bureau  of  Mines  mine-safety  engineer  in  charge  of  breath- 
ing-apparatus  testing,    his   assistants    and   one    representative    of    the 
applicant  will  be  permitted  to  be  present  during  the  conduct  of  the 
tests. 

9.  The  conduct  of  the  tests  shall  be  entirely  under  the  direction   of 
the  bureau's  mine-safety  engineer  in  charge  of  the  testing. 

10.  As  soon  as  possible  after  the  receipt  of  the  formal  application 
for  test,  the  applicant  will  be  notified  of  the  date  on  which  the  test  of  his 
self-contained    mine-rescue    breathing    apparatus    will    begin    and    the 
amount  and  character  of  the  additional  material,  if  any,  it  will  be  neces- 
sary for  him  to  submit. 

11.  The  tests  will  be  made  in  the  order  of  the  receipt  of  the  applica- 
tions for  test,  provided  the  necessary  apparatus  and  material  are  sub- 
mitted at  the  proper  time. 

12.  The  details  of  the  results  of  the  tests  shall  be  regarded  as  con- 
fidential by  all  present  at  the  tests,  and  shall  not  be  made  public  in  any 
way  prior  to  their  official  announcement  by  the  Bureau  of  Mines. 

13.  The  results  of  tests  of  the  breathing  apparatus  that  fail  to  pass 
the  requirements  shall  not  be  made  public  but  shall  be  kept  confidential, 
except  that  the  person  submitting  the  apparatus  will  be  informed  with  a 
view  to  possible  remedy  of  defects  in  future  mine-rescue  breathing  appa- 
ratus submitted,  but  such  changes  will  not  be  permitted  while  testing  is 
in  progress. 

14.  Tests  will  be  made  for  manufacturers  or  accredited  manufacturers' 
agents  and  for  inventors. 

15.  A  list  of  permissible  self-contained  mine-rescue  breathing  appa- 
ratus and  the  results  of  their  tests  will  be  made  public,  from  time  to  time, 
by  the  Bureau  of  Mines. 


150  MINE  GASES  AND  VENTILA  TION 

Character  of  Tests. — After  the  self-contained  mine-rescue  breathing 
apparatus  under  test  for  permissibility  has  been  thoroughly  inspected 
for  mechanical  principles,  a  series  of  fifteen  (15)  working  tests,  each  of 
two  (2)  hours'  duration,  will  be  made.  At  the  beginning  of  the  series  of 
tests,  if  an  oxygen  bottle  is  used  on  thte  apparatus  it  shall  be  first  charged 
with  oxygen  to  a  pressure  of  10  atmospheres  and  the  oxygen  permitted 
to  escape  into  the  air.  The  bottle  used  in  the  tests  shall  be  charged  for 
the  tests  at  a  pressure  prescribed  by  the  manufacturer  of  the  apparatus 
and  shall  be  fully  charged  at  the  beginning  of  each  test.  At  the  be- 
ginning of  each  test  the  breathing  bag  or  bags  shall  be  deflated  to  expel 
any  nitrogen  contained  within. 

A  single  test  must  be  continuous,  without  removal  of  the  apparatus 
from  the  wearer  during,  the  test. 

Samples  of  air  will  be  obtained  from  the  apparatus  on  the  inhalation 
side  of  the  circulatory  system  and  as  near  to  the  mouthpiece  or  the  face 
attachment  as  possible.  The  first  sample  will  be  taken  from  the  oxygen 
bottle  to  be  used  and  just  prior  to  the  beginning  of  the  test.  The 
second  sample  will  be  taken  immediately  after  the  apparatus  has  been 
adjusted  to  the  wearer  and  oxygen  has  been  turned  on.  Samples  will 
be  taken  every  half-hour  thereafter  during  the  test.  The  physiological 
effects  of  the  apparatus  on  the  wearer  will  be  noted  in  each  test. 

Not  more  than  one  test  of  2  hours'  duration  will  be  made  on  any  one 
day.  The  tests  will  be  completed  within  60  days  from  date  of  beginning, 
unless  prevented  by  conditions  arising  which  are  beyond  the  control 
of  the  mine-safety  engineer  in  charge  of  the  tests. 

All  tests  of  apparatus  will  be  conducted  in  a  specially  equipped  gallery 
filled  with  an  irrespirable  atmosphere,  at  the  Pittsburgh  experiment 
station  of  the  Bureau  of  Mines. 

Before  beginning  each  test  the  apparatus  shall  be  examined  and 
tested  to  insure  that  there  is  no  air  leakage  under  working  conditions. 

SPECIFICATIONS  BY  THE  BUREAU  OF  MINES 

In  order  to  receive  the  approval  of  the  Bureau  of  Mines,  self-con- 
tained mine-rescue  breathing  apparatus  must  pass  satisfactorily  each  of 
the  15  tests  required  by  the  bureau  and  meet  the  following  requirements: 

1.  The  amount  of  oxygen  supplied  by  the  apparatus  must  meet  the 
needs  of  the  wearer  at  all  times  during  the  tests. 

2.  The  regenerating  material  shall  absorb,  from  the  expired  air,  carbon 
dioxide  to  the  extent  that  not  more  than  2^  per  cent,  shall  at  any  time 
be  present  in  the  inspired  air.     The  average  shall  not  exceed  1  per  cent, 
for  any  of  the  two-hour  periods  of  test.     This  average  is  to  be  deter- 
mined by  the  analyses  of  air  samples  taken  as  near  the  point  of  inspira- 
tion as  practicable  and  at  uniform  intervals  of  time. 

3.  The  apparatus  shall  be  free  from  mechanical  obstructions  in  order 
that  the  wearer  may  breathe  freely  at  all  times. 


MINE  RESCUE  WORK  AND  APPLIANCES  151 

4.  The  temperature  of  the  inspired  air  must  not  exceed  a  maximum 
of  110  deg.  F.  when  that  of  the  external  air  does  not  exceed  85  deg.  F. 
A  much  lower  temperature  than  110  deg.  F.  for  the  inspired  air  is  de- 
sirable.    Temperature  readings  will  be  taken  at  regular  intervals. 

5.  The  apparatus  shall  be  sufficiently  rugged  in  construction  and  all 
vital  parts  so  protected  as  to  prevent  material  damage  or  wear  to  the 
apparatus  during  the  period  of  tests  to  which  it  will  be  subjected. 

CONSTRUCTION 

1.  The  apparatus  shall  be  designed  to  meet  the  needs  of  the  wearer 
for  not  less  than  a  period  of  two  hours  when  worn  in  irrespirable  air 
without  recharging.     The  apparatus  shall  be  of  a  design  using  a  mouth- 
breathing  device  or  other  face  attachment  that  when  properly  adjusted 
to  the  face  of  the  wearer,  has  a  capacity  of  not  more  than  250  c.c.  of 
dead  space  inside  the, face  attachment  or  mouth-breathing  device,  ex- 
clusive of  tubes  or  connections  thereto. 

Preferably  the  apparatus  shall  not  weigh  more  than  36  pounds  com- 
plete with  headpiece  and  fully  charged,  and  no  apparatus  weighing  more 
than  40  pounds,  complete  with  headpiece  and  fully  charged,  will  be 
accepted  for  final  test. 

2.  The  mechanical  construction  of  the  apparatus  shall  be  such  that 
every  part  can  be  tested,  inspected  and  repaired  by  persons  skilled  in 
such  work,  and  all  parts  which  require  sterilizing  shall  be  readily  accessible 
for  this  purpose. 

3.  All  parts  of  the  apparatus  subject  to  or  liable  to  be  subjected  to 
pressures  in  excess  of  5  pounds  per  square  inch  shall  be  of  such  construc- 
tion or  equipped  with  such  safety  devices  as  shall  insure  the  safety  of  the 
wearer,  as  determined  by  the  15  tests. 

4.  In  apparatus  equipped  with  breathing  bag  or  bags,  or  their  equiva- 
lent, the  inhalation  and  exhalation  compartments  shall  have  a  com- 
bined capacity  of  at  least  8  liters.     If  a  single  breathing  bag  is  used  it 
shall  have  a  capacity  of  at  least  5  liters. 

5.  The  apparatus  shall  not  have  in  its  circulating  system  any  zone  of 
constant  negative  pressure. 

6.  The  apparatus  shall  be  provided  with  a  release  valve,  operated  by 
hand  or  automatically,  placed  at  some  point  in  the  circulatory  system 
of  the  apparatus.     The  function  of  this  valve  shall  be  to  permit  the 
escape  to  the  outside  air  of  a  part  of  the  air  in  the  circulatory  system 
of  the  machine. 

7.  Where  apparatus  is  equipped  with  high-pressure  oxygen  cylinders, 
such  cylinders  shall  be  tested  in  accordance  with  the  Interstate  Commerce 
Commission  specifications  No.  3- A.     Such  tests  shall  be  made  prior  to 
submitting  the  apparatus  to  the  Bureau  of  Mines  for  test  and  the  appli- 
cant submitting  the  apparatus  shall  furnish  the  necessary  certificate  of 
test  as  issued  by  the  Interstate  Commerce  Commission  or  submit  evi- 


152  MINE  GASES  AND  VENTILATION 

dence  satisfactory  to  the  bureau's  mine-safety  engineer  in  charge  of  the' 
testing  of  the  apparatus,  that  such  oxygen  cylinders  have  been  tested  in 
accordance  with  Interstate  Commerce  Commission  specifications  No.  3-^4. 

8.  Where  apparatus  is  equipped  with  high-pressure  oxygen  cylinders 
the  safety  cap  attached  to  the  closing  valve  shall,  in  addition  to  the 
usual  copper  disk  provided,  be  filled  with  a  metal  (such  as  Roses  metal) 
fusing  at  a  temperature  of  approximately  94  deg.  C.     Such  fusible  metal 
shall  not  extrude  from  the  safety  cap  under  a  pressure  of  150  atmospheres. 

9.  The  closing  valve  of  such  oxygen  cylinders  shall  be  provided  with 
the  necessary  device  to  prevent  the  wearer  of  the  apparatus  from  screw- 
ing the  stem  entirely  out  of  the  valve.     The  closing  valve  shall  also  be 
provided  with  such  a  device  as  will  enable  the  wearer  to  lock  the  valve 
stem  when  the  valve  has  been  opened  to  the  desired  point. 

10.  When   apparatus  is  equipped  with  gages  for  recording  time  or 
pressures  of  oxygen  supply,  such  gages  will  be  tested  for  accuracy  of 
calibration  by  the  Bureau  of  Mines.     A  toleration  of  three  atmospheres 
will  be  allowed  in  comparison  with  the  Bureau  of  Mines  standard  pres- 
sure gage. 

11.  The  apparatus  shall  be  supplied  with  a  valve  that  will  cut  off  the 
oxygen  supply  from  the  gage;  this  valve  shall  be  so  placed  that  it  can 
be  readily  manipulated  by  the  wearer  and  at  the  same  time  not  interfere 
with  the  flow  of  oxygen  from  the  oxygen  container  to  the  circulatory 
system  of  the  apparatus. 

12.  The  gage  shall  be  placed  on  the  apparatus  at  such  a  point  that  it 
can  easily  be  read  by  the  wearer. 

13.  Apparatus  equipped  with  a  reducing  valve  giving  a  constant  flow 
of  oxygen  shall  be  provided  with  a  by-pass  valve  which  will  permit  a 
free  flow  of  oxygen  from  the  oxygen  container  to  the  circulatory  system 
of  the  apparatus  independent  of  the  reducing  valve. 

14.  When  the  oxygen  supply  of  the  apparatus  is  controlled  by  auto- 
matic devices,  such  devices  shall  readily  adjust  themselves  to  the  needs 
of  the  wearer. 

15.  When  an  apparatus  is  equipped  with  mouth-breathing  device, 
such  apparatus  shall  be  provided  with  an  adequate  saliva  trap.     The 
adequacy  of  the  saliva  trap  will  be  determined  by  the  tests  to  which  the 
apparatus  will  be  subjected. 

16.  When  an  apparatus  is  equipped  with  mouth-breathing   attach- 
ment, a  suitable  noseclip  shall  be  provided  and  properly  attached  to  the 
apparatus.     The  suitability  of  the  nose  clip  will  be  determined  by  the 
tests  to  which  the  apparatus  will  be  subjected. 

The  apparatus  under  test  will  be  worn  during  each  and  all  of  the  2- 
hour  periods  of  the  15  tests  by  the  Bureau  of  Mines  safety  engineer  in 
charge  of  the  testing  or  by  one  or  more  of  his  assistants.  Immediately 
before  participation  in  any  or  all  of  these  tests  the  prospective  wearer  of 
the  apparatus  under  test  shall  pass,  in  a  satisfactory  manner,  physical 
examination  by  a  qualified  physician.  If  it  is  impossible  to  carry  any 


MINE  RESCUE  WORK  AND  APPLIANCES  153 

one  of  these  tests  to  completion  solely  on  account  of  the  physical  condi- 
tion of  the  wearer,  where  such  condition  has  been  brought  about  through 
no  fault  of  the  apparatus  under  test,  such  test  shall  be  disregarded  and 
the  apparatus  under  test  shall  not  be  penalized  or  disqualified  thereby. 

At  the  conclusion  of  each  test  a  note  shall  be  made  of  the  general 
physical  condition  of  the  apparatus  and  the  amount  of  oxygen,  if  any, 
remaining  in  the  container.  The  schedule  of  work  to  be  performed  by 
the  wearer  of  the  apparatus  in  each  one  of  the  15  working  tests  is  as 
follows: 

Detail  of  Procedure  in  Tests. — Following  is  an  outline  of 
the  manner  of  proceeding  in  the  making  of  each  successive 
test  of  breathing  apparatus  submitted  to  the  bureau. 

Test  1. — The  wearer  of  the  apparatus  shall  walk  continuously,  except 
for  time  necessary  to  take  air  samples  and  temperature  readings,  over  a 
level  measured  course  at  the  rate  of  3^  miles  per  hour.  At  the  end  of 
each  30-minute  period,  2  minutes  shall  be  allowed  for  taking  air  samples 
and  temperature  readings. 

Tests  2,  3,  and  4  will  be  repetitions  of  Test  1. 

Test  5. — In  Test  5  the  wearer  of  the  apparatus  shall — 

(a)  Walk  over  a  level  measured  course  at  a  rate  of  3  miles  per  hour  for 
a  period  of  10  minutes. 

(6)  Carry  a  sack  of  bricks  weighing  50  pounds  over  an  overcast  ten 
times,  making  one  complete  trip  in  2  minutes. 

(c)  Allow   two  minutes  for  taking  of  air  samples  and  temperature 
readings. 

(d)  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 
for  a  period  of  10  minutes. 

(e)  Carry  a  45-pound  weight  a  distance  of  1000  feet,  consuming  5 
minutes  while  doing  this  work. 

(/)  Raise  a  45-pound  weight  through  a  vertical  distance  of  5  feet  75 
times,  consuming  5  minutes  while  doing  this  work. 

(g)  Saw  wood  for  a  period  of  10  minutes. 

(h)  Allow  two  minutes  for  taking  of  air  samples  and  temperature 
readings. 

(i)  Carry  a  sack  of  bricks  weighing  50  pounds  over  an  overcast  10 
times,  making  one  complete  trip  in  2  minutes. 

0')  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 
until  the  end  of  the  2  hours  allowed  for  this  test,  air  and  temperature 
readings  to  be  taken  in  2-minute  periods  at  1^  and  2  hours  after  start 
of  test. 

Tests  6,  7,  and  8  will  be  repetitions  of  Test  5. 

Test  9. — In  Test  9  the  wearer  of  the  apparatus  shall — 

(a)  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 
for  a  period  of  10  minutes. 


154  MINE  GASES  AND  VENTILATION 

(6)  Crawl  for  a  distance  of  100  feet,  consuming  5  minutes  while  doing 
this  work. 

(c)  Lie  down  on  side  for  5  minutes. 

(d)  Lie  down  on  back  for  5  minutes. 

(e)  Allow  2  minutes  for  taking  of  air  samples  and  temperature  readings. 
(/)  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 

for  a  period  of  10  minutes. 

(g)  Run  600  feet  at  a  rate  of  6  to  8  miles  per  hour  over  a  level  mea- 
sured course,  consuming  2  minutes  while  doing  this  work. 

(h)  Walk  1000  feet  over  a  level  measured  course  at  the  rate  of  approxi- 
mately 3  miles  per  hour,  consuming  4  minutes  while  doing  this  work. 

(i)  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 
until  end  of  the  2  hours  allowed  for  this  test.  Air  and  temperature  read- 
ings to  be  taken  in  2-minute  periods  at  one  hour,  1J£  hours  and  two 
hours  after  the  beginning  of  the  test. 

Tests  10  and  11  will  be  repetitions  of  Test  9. 

Test  12. — In  Test  12  the  wearer  of  the  apparatus  shall— 

(a)  Walk  1000  feet  at  the  rate  of  approximately  3  miles  per  hour 
over  a  level  measured  course,  consuming  4  minutes  while  doing  this 
work. 

(6)  Run  600  feet  at  a  rate  of  6  to  8  miles  per  hour  over  a  level  measured 
course,  consuming  2  minutes  while  doing  this  work. 

(c)  Walk    1000  feet  at  the  rate  of  3  miles  per  hour  over  a  level  mea- 
sured course,  consuming  4  minutes  while  doing  this  work. 

(d)  Raise  a  45-pound  weight  75  times  through  a  vertical  distance  of 
5  feet,  consuming  5  minutes  while  doing  this  work. 

(e)  Carry  a  45-pound  weight  over  a  level  measured  course   1000 
feet,  consuming  5  minutes  while  doing  this  work. 

(/)  Carry  a  sack  of  bricks  weighing  50  pounds  over  an  overcast  5 
times,  making  one  complete  trip  in  2  minutes. 

(0)  Allow  2  minutes  for  taking  of  air  samples  and  temperature  readings. 
(h)  Raise  a  45-pound  weight  75  times  through  a  vertical  distance  of 

5  feet,  consuming  5  minutes  while  doing  this  work. 

(1)  Walk  over  a  measured  course  at  rate  of  3  "miles  per  hour  for  a 
period  of  10  minutes. 

(j)  Carry  a  sack  of  bricks  weighing  50  pounds  over  an  overcast  10 
times,  making  one  complete  trip  in  1^  minutes. 

(fc)  Allow  2  minutes  for  taking  of  air  samples  and  temperature  readings. 

(/)  Walk  1000  feet  at  rate  of  approximately  3  miles  per  hour  over  a 
level  measured  course,  consuming  4  minutes  while  doing  this  work. 

\m)  Raise  a  45-pound  weight  75  times  through  a  vertical  distance  of 
5  feet  consuming  5  minutes  while  doing  this  work. 

(n)  Walk  at  the  rate  of  3  miles  per  hour  over  a  level  measured  course 
until  the  end  of  the  two  hours  allowed  for  this  test.  Air  and  temperature 
readings  are  to  be  taken  in  2-minute  periods  at  1^  and  2  hours  after 
the  start  of  the  test. 


MINE  RESCUE  WORK  AND  APPLIANCES  155 

Tests  13  and  14  will  be  repetitions  of  Test  12. 

Test  15. — This  test  will  be  made  to  determine  the  maximum  length 
of  time  that  the  apparatus  will  supply  the  needs  of  the  wearer  when  in  a 
quiescent  state.  The  wearer  will  remain  as  far  as  possible  in  a  sitting 
posture  throughout  the  test  and  perform  no  work.  He  will  be  allowed  to 
manipulate  the  devices  controlling  the  oxygen  supply  with  a  view  to 
conserving  such  oxygen  supply  to  the  greatest  advantage. 

At  the  end  of  each  30-minute  period,  2  minutes  shall  be  allowed  for 
taking  of  air  samples  and  temperature  readings. 

NOTE. — Self-contained  mine-rescue  breathing  apparatus  in 
course  of  development  may  be  submitted  by  manufacturers 
and  inventors  for  preliminary  test  or  inspection  with  the  view 
of  ascertaining  defective  construction  or  the  misapplication  of 
safety  principles.  The  nature  of  such  tests  or  inspection  will 
be  determined  by  the  bureau's  mine-safety  engineer  in  charge 
of  the  testing  of  such  apparatus. 

Approval  of  Apparatus. — The  manufacturers  of  such  types  of  self- 
contained  mine-rescue  breathing  apparatus  as  have  passed  the  tests  of 
the  bureau  will  be  required  to  attach  to  each  apparatus  a  plate  containing 
the  following  inscription: 

Permissible    Mine-Rescue    Breathing    Apparatus, 
U.   S.   Bureau  of  Mines  Approval  No.  _  . 

The  use  of  the  plate  will  .not  be  required  if  the  same  inscription  is 
stamped  or  cast  into  the  metal  of  the  apparatus. 

Manufacturers  shall,  before  claiming  the  bureau's  approval  for  any 
modification  of  a  permissible  self-contained  mine-rescue  breathing  appa- 
ratus, submit  to  the  Bureau  drawings  or  parts  that  shall  show  the  extent 
and  nature  of  such  modifications,  in  order  that  the  bureau  may  decide 
whether  test  of  the  remodeled  apparatus  will  be  necessary  for  approval. 
If  it  is  decided  by  the,  bureau  that  testing  of  the  remodeled  apparatus 
is  necessary,  the  word  "permissible"  shall  not  be  used  on  the  remodelled 
apparatus  until  it  has  again  passed  the  complete  schedule  of  tests  or  such 
part  of  these  tests  as  the  bureau's  engineer  in  charge  of  the  tests  shall 
deem  necessary. 

The  bureau  will,  on  application,  make  separate  tests,  identical  with  the 
foregoing  tests,  of  regenerators  manufactured  for  use  in  connection 
with  any  mine-rescue  breathing  apparatus  that  has  been  approved  by  the 
bureau  under  the  provisions  of  this  schedule. 

Regenerators  that  fulfill  the  requirements  of  the  foregoing  tests  will 
be  approved  for  use  only  in  connection  with  that  particular  type  of 
apparatus  for  which  they  are  designed  and  which  has  previously  re- 
ceived the  bureau's  approval. 


156  MINE  GASES  AND  VENTILATION 

The  listing  by  the  Bureau  of  Mines,  as  "permissible,"  any  self-con- 
tained mine-rescue  breathing  apparatus  shall  be  construed  as  applying 
only  to  apparatus  of  that  specific  type,  class,  form  and  rating,  made  by 
the  same  manufacturer,  which  have  the  same  construction  in  all  details 
directly  or  indirectly  affecting  the  safety  features  of  the  apparatus. 

The  bureau  reserves  the  right  to  rescind  for  cause,  at  any  time,  any 
approval  granted  under  the  conditions  herein  set  forth.  Cause  for 
rescinding  of  approval  shall  be  considered  to  be  the  use  of  the  bureau's 
issuance  of  approval  in  an  unauthorized  manner;  that  is,  placing  the 
approval  stamp  on  apparatus  that  has  not  been  approved  by  the  bureau, 
or  on  apparatus  certain  parts  of  which  have  been  altered  in  construction 
or  material  without  submittal  to  the  bureau  for  test. 

Notification  to  Manufacturer. — As  soon  as  the  mine-safety  engineer  of 
the  Bureau'of  Mines  is  satisfied  that  a  self-contained  mine-rescue  breath- 
ing apparatus  has  passed  all  the  tests  herein  set  forth  in  a  satisfactory 
manner,  the  manufacturer  or  inventor  shall  be  formally  notified  to  that 
effect. 

When  two  or  more  applications  for  tests  on  different  apparatus  are 
received  within  a  period  of  10  days,  the  announcement  of  approval  for 
each  shall  not  exceed  the  interval  of  time  between  the  receipt  of  the 
applications. 

When  a  manufacturer  or  inventor  receives  this  formal  notification  he 
shall  be  free  to  advertise  this  type  of  successfully  tested  self-contained 
mine-rescue  breathing  apparatus  as  permissible  according  to  the  Bureau 
of  Mines  standards  and  may  attach  approval  plates  to  this  type  of 
breathing  apparatus. 

Fees  for  Testing. — Careful  investigation  has  been  made  regarding  the 
necessary  expenses  involevd  in  testing  mine-rescue  breathing  apparatus, 
at  the  Pittsburgh  experiment  station  of  the  bureau.  The  following 
schedule  of  fees  to  cover  expenses  to  be  charged  on  and  after  March  5, 
1919  has  been  established  and  approved  by  the  Secretary  of  the  Interior, 
in  accordance  with  the  provisions  of  the  statute  previously  quoted, 

Complete  mine-rescue  breathing  apparatus  test $100 

Separate  preliminary  inspection  and  test $10 

Separate  regenerator  test $5 

Separate  inspection  and  test  of  reducing  valves $10 

The  fees  specified  above  may  be  increased  to  cover  the  cost  of  testing 
an  unusually  complicated  type  of  mine-rescue  breathing  apparatus,  and 
are  also  subject  to  change  upon  the  recommendation  of  the  Director  of 
the  Bureau  of  Mines  and  the  approval  of  the  Secretary  of  the  Interior. 

Application  for  Test  of  Apparatus. — 1.  Application  for  tests  should  be 
addressed  to  the  director  of  the  Bureau  of  Mines,  Washington,  D.  C. 
This  application  must  be  accompanied  by  check  or  draft  made  payable 
to  the  Secretary  of  the  Interior,  and  by  a  complete  written  description  of 
the  mine-rescue  breathing  apparatus  to  be  tested,  and  a  set  of  the  drawings 


MINE  RESCUE  WORK  AND  APPLIANCES  157 

as  specified  in  the  Conditions  of  Testing,  page  148,  and  marked  "  Drawings 
of  Approved  Mine-Rescue  Breathing  Apparatus  to  be  Filed."  Duplicate 
copies  of  the  application  and  drawings  should  be  sent  to  the  mine-safety 
engineer,  Bureau  of  Mines,  Pittsburgh,  Penn. 

2.  As  soon  as  the  application  is  received  by  the  bureau's  mine-safety 
engineer,  the  applicant  will  be  notified  of  the  date  the  tests  will  begin. 

3.  After  the  applicant  has  received  this  notification,  he  should  send  the 
material  required  to  the  mine -safety  engineer,  Bureau  of  Mines,  Pitts- 
burgh, Penn.     This  material  should  be  delivered  not  less  than  one  week  in 
advance  of  the  date  set  for  the  beginning  of  the  tests. 

4.  The  tests  will  be  begun  on  the  date  set  and  continued  until  the  mine- 
rescue  breathing  apparatus  has  been  approved,  rejected  or  withdrawn. 

5.  After  the  bureau's  mine-safety  engineer  has  considered  the  results 
of  the  tests,  a  formal  report  of  the  approval  of  the  self-contained  mine- 
rescue  breathing  apparatus  will  be  made  to  the  applicant,  in  writing,  by 
the  director  of  the  Bureau  of  Mines.     No  verbal  report  will  be  made,  and 
the  details  of  the  test  will  be  regarded  as  confidential  by  all  present. 
Approved  March  5,  1919. 

.8.  G.  HOPKINS,  VAN  H.  MANNING, 

Assistant  Secretary.  Director. 

FIRST-AID  WORK 

Practical  Use  of  Breathing  Apparatus. — It  is  of  the  greatest 
importance  that  all  breathing  apparatus  should  be  carefully 
examined  and  tested  before  the  wearer  proceeds  to  enter  an 
irrespirable  atmosphere.  First,  it  is  necessary  to  observe  the 
gage  or  meter  to  see  that  the  proper  supply  of  oxygen  is  con- 
tained in  the  oxygen  cylinder.  Observe  also  that  the  required 
quantity  of  oxygen  (2  liters)  is  being  delivered  each  minute,  as 
indicated  by  a  registering  meter.  The  breathing  bag  must  be 
carefully  tested  and  all  valves  examined  to  see  that  they  are  in 
good  working  condition  and  to  ascertain  that  the  breathing  bag 
contains  no  airleaks. 

In  use,  always  inflate  the  bag  with  pure  air  when  ready  to 
put  on  the  apparatus  and  before  turning  on  the  supply  of  oxy- 
gen. It  is  well  for  the  wearer,  then,  to  take  the  precaution 
of  going  into  a  smoke  chamber,  for  a  short  period  before  enter- 
ing the  mine.  This  will  enable  him  to  ascertain  that  there  are 
no  leaks  in  the  apparatus  and  that  breathing  is  normal. 

Resuscitation. — To  resuscitate  is  to  revive,  or  to  restore 
animation  in  an  unconscious  person  or  one  who  is  seemingly 


158  MINE  GASES  AND  VENTILA  TION 

dead.  A  person  may  be  apparently  lifeless  as  the  result  of  any 
one  of  several  causes;  (1)  Fainting  from  overexertion.  2. 
The  result  of  a  nervous  shock.  3.  An  electric  shock,  received 
by  contact  with  a  live  wire.  4.  Suffocation,  by  reason  of  in- 
haling irrespirable  gases,  or  the  lungs  being  filled  with  water, 
as  in  drowning.  5.  A  blow  on  the  head.  In  fact,  unconscious- 
ness may  result  from  any  accidental  occurrence  affecting  di- 
rectly or  indirectly  the  nervous  system  on  which  respiration 
and  animation  depends. 

In  the  work  of  resuscitation,  due  regard  must  always  be  had 
to  the  cause  of  suspended  animation.  Where  the  lungs  have 
filled  with  water,  as  in  drowning,  or  with  gas  inhaled  in  the 
mine  or  elsewhere,  immediate  steps  must  be  taken  to  drive  the 
water  or  gas  from  the  lungs  and  permit  the  entry  of  fresh  air 
through  artificial  respiration  applied  vigorously  and  continued 
till  the  person  revives,  or  it  is  absolutely  certain  that  life  is 
extinct.  If  the  trouble  arises  from  the  inhalation  of  gas, 
the  victim  must  be  removed  promptly  to  fresh  air  before  treat- 
ment is  administered,  loosen  the  clothing  about  the  neck  and 
chest  and  give  artificial  respiration,  at  the  same  time  chafing 
the  limbs,  rubbing  them  toward  the  body  to  assist  the  flow  of 
the  venous  blood  back  to  the  heart. 

Smelling  salts  applied  to  the  nostrils  assist  to  quicken  ani- 
mation. As  soon  as  the  victim  is  able  to  swallow  and  on  the 
first  signs  of  returning  life,  give  a  stimulant,  hot  coffee  or  tea, 
or  half  a  teaspoonful  of  aromatic  spirits  of  ammonia  in  a 
half-glass  of  water,  administered  in  small  doses  at  slight 
intervals.  Where  shock  has  resulted  from  injury  and  loss  of 
blood,  however,  stimulants  should  not  be  given,  as  these  will 
assist  the  action  of  the  heart  and  increase  the  flow  of  blood 
from  the  wound.  In  all  other  cases,  return  of  animation  will 
be  assisted  by  any  means  that  will  assist  the  circulation  of  blood 
and  revive  the  respiratory  system.  Keep  the  patient  warm 
with  blankets  and  give  plenty  of  fresh  air  during  treatment 
for  resuscitation. 

•Artificial  Respiration. — -There  are  two  general  methods  of 
applying  artificial  respiration.  In  the  Sylvester  method, 
which  is  now  little  used,  the  patient  is  laid  on  his  back,  while 


MINE  RESCUE  WORK  AND  APPLIANCES  159 

the  operator  kneeling  at  his  head  grasps  the  wrists  of  both 
arms  and  proceeds  to  alternately  swing  the  arms,  first  forward 
on  the  chest  and  then  back  to  a  position  above  the  head,  at 
the  normal  rate  of  breathing  or,  say  16  times  a  minute.  In 
the  forward  movement,  the  arms  are  doubled  at  the  elbow  and 
pressed  down  firmly  against  the  sides  of  the  chest  so  as  to 
compress  the  lungs  and  force  out  the  gas  therefrom.  This  is 
followed  by  the  backward  movement,  which  has  the  effect 
of  expanding  the  lungs  and  inducing  inhalation.  These  move- 
ments are  continued  alternately,  first  compressing  the  lungs 
and  then  expanding  them  in  turn.  While  doing  this,  it  is 


m 


important  to  secure  the  tongue  and  hold  it  forward  in  the 
mouth  so  that  it  will  not  impede  the  access  of  air  to  the  lungs. 
A  handkerchief  covering  the  fingers  will  help  to  hold  the  ton- 
gue forward,  or  a  clip  must  be  used  for  that  purpose. 

The  common  method  of  resuscitation  now  most  generally 
employed  is  that  known  as  the  "Schaefer  method,"  or  the 
" prone  method"  of  resuscitation.  By  this  method,  the  pa- 
tient is  laid  prone  on  his  face,  except  that  the  head  is  turned 
to  one  side  to  facilitate  breathing.  The  operator,  having  made 
sure  that  the  tongue  is  drawn  forward  in  the  mouth  so  as  to 
give  free  access  of  air  to  the  lungs,  straddles  the  patient's 
thigh,  as  shown  in  Fig.  20,  and  rests  the  -palms  of  his  hands 


160  MINE  GASES  AND  VENTTLA TION 

on  the  person's  loins  with  the  two  thumbs  together  and  the 
fingers  reaching  well  down  on  each  side,  in  a  manner  to  bring 
pressure  on  the  short  ribs  and  across  the  small  of  the  back. 

In  this  position,  the  operator  first  swings  forward  so  as  to 
throw  his  weight  on  the  patient's  body  compressing  the  lungs 
to  drive  out  the  gas  or  water  they  contain.  Then,  swinging 
backward,  he  gives  opportunity  for  the  expansion  of  the  lungs, 
which  induces  the  inhalation  of  fresh  air.  As  in  the  Sylvester 
method,  this  forward  and  backward  movement  must  be 
continued  alternately,  for  a  period  of  an  hour  or  two,  until 
there  are  signs  of  returning  life  or  it  is  absolutely  necessary 
that  life  is  extinct.  There  are  instances  on  record  where  the 
victim  has  been  revived  after  several  hours  of  hard  work. 
It  is  often  necessary  for  the  operator  to  be  relieved  for  a  time 
by  another,  but  the  process  must  be  continued  without  cessa- 
tion, until  a  doctor  gives  it  as  his  opinion  that  life  has  fled. 
In  every  case,  send  for  a  doctor  while  giving  first-aid  to  the 
patient. 


SECTION  VI 
THEORY  OF  VENTILATION 

MINE  VENTILATION — PROBLEMS — FLOW  OF  Am  IN  AIRWAYS 
— VENTILATING  PRESSURE,  How  PRODUCED  AND  MEAS- 
URED, THE  WATER  GAGE — VELOCITY  OF  AIR  CURRENTS 
— QUANTITY  OF  AIR,  REQUIREMENTS — WORK  OR  POWER 
ON  THE  AIR — EQUIVALENTS  IN  MEASUREMENT — EXAM- 
PLES FOR  PRACTICE — MINE  AIRWAYS — SYMBOLS  AND  FOR- 
MULAS— MINE  POTENTIAL  METHODS — MEASUREMENT  OF 
AIR  CURRENTS — EXAMPLES  FOR  PRACTICE — TANDEM  CIR- 
CULATIONS— SPLITTING  THE  AIR  CURRENT — NATURAL 
DIVISION  OF  AIR — EXAMPLES  IN  NATURAL  DIVISION- 
PROPORTIONATE  DIVISION  OF  AIR,  REGULATORS — SECOND- 
ARY SPLITTING — THEORETICAL  CONSIDERATIONS  IN 
SPLITTING — PRACTICAL  PROBLEM 

MINE  VENTILATION 

The  ventilation  of  a  mine,  as  the  term  implies,  involves 
the  supply  and  maintenance  of  a  sufficient  current  of  air 
throughout  the  mine  to  render  the  same  healthful  and  safe. 

Requirements  of  Ventilation. — The  quantity  of  air  in  circu- 
lation must  be  sufficient  to  comply  with  the  state  mining  law, 
and  to  dilute,  render  harmless  and  sweep  away  the  gases 
that  would  otherwise  accumulate  in  the  mine.  The  air  cur- 
rent must  be  conducted  so  as  to  sweep  the  entire  working 
face  and  all  void  places  with  a  moderate  velocity  sufficient 
to  remove  the  gas  without  danger  from  the  lamps  or  inconven- 
ience to  the  workmen. 

The  Circulating  System. — In  order  to  circulate  a  current  of 
air  through  a  mine,  it  is  necessary  to  provide  two  separate 
openings,  one  for  the  air  to  enter,  called  the  "intake  opening," 
and  the  other  for  it  to  leave  the  mine,  called  the  " return"  or 
"  discharge  opening.".  Two  distinct  air  passages  or  airways 
are  also  required,  leading  from  these  openings  into  the  mine, 
in  order  to  conduct  the  air  current  to  and  from  the  working 
n  161 


162 


MINE  GASES  AND  VENTILATION 


face.  These  are  called,  respectively,  the  "intake"  and  "re- 
turn "  airways.  These  openings  and  airways  form  a  part  of  the 
circulating  system  in  the  mine,  similar  to  the  arteries  and  veins 
of  the  human  body. 

Kinds  of  Ventilation. — There  are  three  different  kinds  of 
ventilation-,  in  mining  practice,  known  as  "  natural  ventila- 
tion," "furnace  ventilation"  and  mechanical  or  "fan  ventila- 
tion," according  to  the  agency  employed  for  its  production. 

Natural  Ventilation. — Ventilation  is  natural  when  it  is 
produced  by  any  natural  agency,  such  as  surface  winds, 
falling  water  or  the  natural  heat  of  the  mine.  The  accompany- 
ing Fig.  21  illustrates  the  manner  in.  which  the  natural  heat  of 
the  mine  produces  a  warm  upcast  air  column,  in  either  a  drift 
mine  or  a  shaft  mine. 


Surface 


FIG.  21. 

In  the  drift  mine  shown  on  the  left,  the  warmer  air  column 
in  the  shaft  only  partly  balances  the  cooler  outside  air.  Above 
the  level  of  the  top  of  the  shaft  the  two  air  columns  are  of  equal 
temperature  and  equal  weight,  and,  therefore,  need  not  be 
considered  since  they  balance  each  other.  The  same  is  true 
in  the  shaft  mine  shown  on  the  right,  whenever  the  two  shafts 
have  the  same  elevation  at  the  surface. 

Natural  Ventilation  in  Slope  Mines  and  Dip  Workings.— 
A  similar  condition  in  respect  to  the  natural  heat  of  the  mine 
producing  or  modifying  the  circulation  of  the  air,  holds  in 
all  slope  mines  and  dip  workings,  the  same  as  in  shafts  and 
drifts.  Whenever  the  mine  temperature  is  much  below  or 
above  that  of  the  outside  atmosphere,  the  difference  in  tem- 
perature makes  the  return  air  heavier  or  lighter  than  the 


THEORY  OF  VENTILATION  163 

intake  air;  and  the  difference  in  weight  of  these  two  air  col- 
umns destroys  the  equilibrium  of  the  mine  air  and  creates 
a  current  in  the  airways  throughout  the  mine. 

A  considerable  difference  of  temperature  is  often  observed 
between  the  dip  and  rise  air  currents  in  particular  sections 
of  a  mine.  It  is  this  difference  in  the  temperatures  of  the 
intake  and  return  currents  that  often  makes  dip  workings 
harder  to  ventilate  in  summer  than  in  winter.  For  the  same 
reason,  rise  workings  are  frequently  found  to  be  more  easily 
ventilated  in  the  summer  season. 

Air  Columns.  —  The  term  "air  column,"  like  water  column, 
always  refers  to  a  vertical  column.  The  air  column,  in  ven- 
tilation, is  an  imaginary  vertical  column  of  air,  of  unit  sec- 
tion (commonly,  1  sq.  ft.)  and  of  such  height  that  its  weight, 
in  pounds,  is  equal  to  the  pressure  it  measures  (Ib.  per  sq.  ft.). 
The  density  of  the  air  (wt.  per  cu.  ft.)  is  either  stated  or  under- 
stood, so  that  when  the  height  of  air  column  is  given  the 
pressure  it  indicates  is  readily  calculated. 

In  mining  practice,  it  is  common  to  express  ventilating 
pressure  in  feet  of  air  column  or,  as  we  say,  "head  of  air." 
Calling  the  weight  of  1  cu.  ft.  of  air  w  (Ib.)  and  the  head  of 
air  column  h  (ft.),  the  pressure  p  (Ib.  per  sq.  ft.)  is  calculated 
by  the  formula 

p  =  wh 

Or  the  air  column  corresponding  to  any  given  pressure  is 
found  by  transposing  this  formula;  thus, 


w 

Example.  —  What  is  the  head  of  air  column  corresponding  to  a  ventilat- 
ing pressure  of  10  Ib.  per  sq.  ft.,  assuming  a  temperature  of  60  deg.  F. 
and  a  barometric  pressure  of  30  in.? 

Solution.  —  The  weight  of  1  cu.  ft.  of  air,  at  the  given  temperature  and 
pressure  is 

1.3273J3        1.3273  X  30 


460-+1  6 

The  required  head  of  air  is  then 


°-°766 


~  =  ?Ti^  =  130.5  /«. 
w        0.0766 


164  MINE  GASES  AND  VENTILA  TION 

Example. — Find  the  ventilating  pressure  and  water  gage  corresponding 
to  80  ft.  of  air  column,  &t  the  same  density. 
Solution. — 

p       =  Wh  =  0.0766  X  80  =  6.128  Ib.  per  sq.  ft. 

w.g.  =  6.128  -T-  5.2  =  1.18  in.,  nearly 

Furnace  Ventilation. — When  the  circulation  of  air  through- 
out a  mine  is  created  and  maintained  by  means  of  a  furnace 
built  in  the  mine  the  system  is  known  as  "  Furnace 
ventilation." 

Principle  of  Furnace  Ventilation. — The  heat  of  the  furnace 
imparted  to  the  air  in  the  furnace  shaft  makes  it  lighter, 
volume  for  volume,  which  causes  it  to  rise  in  obedience  to 
the  law  of  the  equilibrium  of  fluids.  The  cooler  and  heavier 
outside  air,  in  obedience  to  the  same  law,  flows  into  the  mine  by 
way  of  another  opening,  to  take  the  place  of  the  air  displaced. 
The  action  is  continuous  as  long  as  the  furnace  is  in  operation. 
There  is  thus  created  and  maintained  a  constant  flow  of  air 
into  and  through  the  mine. 

Location  of  a  Mine  Furnace. — The  furnace  is  built  in  the 
main-return  airway  about  20  or  25  yd.  back  from  the  foot  of 
the  upcast  or  furnace  shaft,  so  as  to  reduce  the  danger  of  the 
fire  damaging  or  destroying  the  shaft. 

Construction  of  Furnace. — The  essential  details  to  be  con- 
sidered in  the  construction  of  an  efficient  mine  furnace  are 
the  following: 

1.  Beginning,  say  50  yd.  back  from  the  foot  of  the  shaft, 
the  main-return  airway  should  be  gradually  widened  and  its 
height  increased  so  that  the  unobstructed  sectional  area  at 
the  furnace  will  not  be  less  than  25  per  cent,  greater  than 
that  of  the  original  airway. 

2.  The  roof  of  the  enlarged  airway  should  then  be  se- 
cured by  steel  rails  or  I  beams  supported  on  posts  or  concrete 
walls,  as  illustrated  in  Pig.  22,  which  represents  a  well  built 
mine  furnace. 

3.  As  shown  in  the  figure,  both  the  concrete  walls  and  the 
brick  walls  supporting  the  arch  are  started  on  a  good  firm 
bottom  below  the  floor  line.     The  thickness  of  the  concrete 
walls  will  vary  from  10  or  12  in.  to  2  ft.,  depending  on  depth 


THEORY  OF  VENTILATION 


165 


of  cover  and  other  roof  conditions.  The  brick  walls  and  arch 
will  vary  in  thickness  from  8  to  12  in.  A  good  quality  of 
vitrified  brick  should  be  used,  except  where  the  arch  and 
walls  are  exposed  to  the  direct  action  of  the  flame  they  should 
be  lined  with  the  best  firebrick.  All  bricks  should  be  first 
soaked  in  water  before  being  laid  and  only  the  best  cement 
mortar  should  be  used. 

4.  The  brick  walls  and  arch  should  be  started  about  2  yd. 
in  front  of  the  furnace  proper  and  extended  to  the  face  of 
the  shaft.  The  clear  width  between  the  walls  should  equal 
the  width  of  the  fire-grate,  and  should  be  such  as  to  leave 
a  clear  passageway  between  the  brick  and  concrete  walls. 


CROSS- SECTION  LONGITUDINAL  SECTION   ON  CENTER  LINE 

THROU&H  FURNACE  OF  ENTRY 

FIG.  22. 

The  arch  is  semicircular  and  sprung  at  such  a  height  above 
the  floor  as  to  leave  not  less  than  12  in.  of  space  between  the 
crown  of  the  arch  and  the  rails  that  support  the  roof.  The 
purpose  of  this  air  space  around  the  furnace  is  to  isolate  the 
heat,  which  is  thus  more  completely  utilized  in  heating  the 
air  current. 

5.  The  area  of  the  grate  or  the  grate  surface  must  be 
sufficient  to  burn  the  weight  of  coal  per  hour  required  to  heat 
the  volume  of  air  passing  the  furnace  in  that  time,  to  a  tem- 
perature that  will  create  the  air  column,  in  a  given  depth 
and  condition  of  shaft,  necessary  to  circulate  such  volume  of 
air  against  a  specified  mine  potential. 

The  theoretical  problem  of  determining  the  weight  of  coal 
burned  per  hour,  per  volume  of  air  circulated,  is  thus  seen  to 
depend  on  many  factors.  In  ordinary  mining  practice,  how- 
ever, a  safe  estimate  is  to  assume  that  each  pound  of  coal 
burned  per  hour  will  cause  a  rise  in  temperature  of  from  10 


166  MINE  GASES  AND  VENTILATION 

to  15  deg.  F.,  per  1000  cu.  ft.  of  air  in  circulation.  Or,  calling 
the  weight  of  coal  burned  W  (Ib.  per  hr.);  the  volume  of  air 
passing  Qm  (1000  cu.  ft.  per  min.);  the  rise  in  temperature  t 
(deg.  F.),  and  the  temperature  constant  c  =  10  to  15  deg.  F., 


Example.  —  Find  the  weight  of  coal  required  per  hour,  to  produce  a 
rise  of  temperature  of  360  deg.  F.,  in  a  furnace  shaft  when  a  current  of 
100,000  cu.  ft.  of  air  per  minute  is  passing,  under  fair  mining  conditions. 

Solution.  —  The  weight  of  coal  required  is 

Qmt        100  X  360 
TV   =  ~—  =  ----  -  2  --  =  3000  Ib.  per  hr. 

In  very  deep  or  wet  shafts  or  a  comparatively  small  mine 
resistance,  giving  a  larger  air  volume  and  greater  loss  of 
heat,  the  constant  10  deg.  should  be  used;  while  in  dry  shafts 
of  less  depth,  especially  if  the  mine  resistance  is  considerable, 
a  temperature  constant  of  15  or  even  16  may  be  employed  to 
find  the  necessary  weight  of  coal. 

6.  The  grate  area  necessary  to  burn  any  required  weight 
of  coal  W  (Ib.  per  hr.)  varies  with  the  hardness  and  the  inflam- 
mability of  the  coal.  A  mine  furnace  will  commonly  burn 
from  15  to  20  Ib.  of  anthracite,  or  from  20  to  25  Ib.  of  bitumin- 
ous coal,  per  square  foot  of  grate,  per  hour.  Hence  the  weight 
of  coal  required,  divided  by  such  constant  will  give  the  neces- 
sary area  of  grate  surface,  in  square  feet. 

Example.  —  What  grate  area  will  be  required  to  burn,  say  3000  Ib.  of  a 
very  soft,  inflammable  coal  per  hour? 

Solution.  —  In  this  case,  the  coal  being  a  free-burning,  inflammable 
coal,  the  constant  25  should  be  used;  and  the  required  area  is  3000  •*-  25 
=  120  sq.ft. 

Estimation  of  Air  Columns  in  Practice.  —  In  the  ventila- 
tion of  shaft  or  slope  mines  or  rise  and  dip  workings  in  in- 
clined seams,  the  weight  of  each  respective  downcast  and 
upcast  column  is  sometimes  calculated  separately,  by  multi- 
plying the  weight  of  1  cu.  ft.  of  air,  at  a  barometric  pressure 
B  and  a  temperature  t  equal  to  the  average  temperature  of 


THEORY  OF  VENTILATION 


167 


the  column,  by  the  height  or  ojepth  D  of  the  same  column,  as 
expressed  by  the  formula 

1.3273B 


= 


All  air  columns  are  of  unit  cross-section  (1  sq.  ft.)  and  the 
calculated  weight  of  the  column,  therefore,  gives  the  corre- 
sponding pressure  in  pounds  per  square  foot. 

Positive  and  Negative  Air  Columns.  —  An  air  column  that 
acts  to  assist  the  circulation  in  the  mine  or  airway  is  called 
a  "  positive"  column;  while  one  that  acts  to  oppose  the  cir- 
culation is  termed  a  "negative"  column.  In  fan  ventilation, 
a  negative  air  column  may  exist  in  the  downcast  shaft  by  rea- 
son of  its  temperature  being  greater  than  that  of  the  upcast, 
which  frequently  happens  in  the  summer  season. 


Conditions. — The  height  or  depth  D  of  air  column,  in  any 
particular  case,  can  only  be  determined  by  carefully  consider- 
ing the  conditions.  It  is  important  to  remember  that,  with 
few  exceptions,  the  temperature  of  a  downcast-shaft  column 
will  closely  approximate  that  of  the  outer  air  with  which  this 
shaft  is  constantly  filled;  while  the  temperature  of  the  up- 
cast column  is  practically  determined  by  that  of  the  mine  or, 
in  furnace  ventilation,  by  the  furnace. 

When  two  shafts,  upcast  and  downcast,  Fig.  23,  (a),  are  sunk 
from  a  level  surface  or,  in  other  words,  have  the  same  surface 
elevation  it  is  evident  that  this  level  marks  the  upper  limit 
of  both  columns. 

When,  however,  the  two  shafts  are  sunk  on  a  hillside  and 
have  different  surface  elevations,  two  cases  may  arise,  as  il- 
lustrated in  Fig.  22,  (6)  and  (c),  in  which,  for  the  sake  of  clear- 


1G8  MINE  GASES  AND  VENTILA TION 

ness,  the  outside  temperature  is  Assumed  as  32  deg.  F.  and  that 
of  the  mine  as  60  deg.  F. 

The  two  cases  are  as  follows : 

"l.  When  the  shaft  having  the  higher  surface  elevation  is 
made  the  upcast,  as  is  usually  done,  that  elevation  marks  the 
upper  limit  of  both  shaft  columns;  because  the  downcast 
shaft  has  practically  the  same  temperature  as  the  outer  air. 

2.  When  the  shaft  having  the  lower  surface  elevation  is 
made  the  upcast  this  elevation  marks  the  upper  limit  of  both 
shaft  columns;  because  the  air  in  the  other  (downcast)  shaft 
above  this  level  is  balanced  by  the  corresponding  column  of 
outside  air. 

These  two  conditions,  therefore,  are  simply  expressed  by 
the  statement  that,  in  either  case,  the  upper  limit  of  both 
shaft  columns  is  the  surface  level  of  the  upcast  shaft. 

In  the  same  manner  it  can  be  shown  that  the  lower  limit 
of  both  shaft  columns  is  the  bottom  of  the  downcast  shaft 
when  the  seam  has  a  general  inclination.  Hence,  the  length 
(D)  of  both  shaft  columns  is  measured,  in  any  case,  from  the 
top  of  the  upcast  to  the  bottom  of  the  downcast  shaft.  This 
rule  does  not  apply  to  slopes. 

Ventilating  Pressure  and  Shaft  Columns. — Since  the  weight 
of  an  air  column,  in  pounds,  expresses  the  corresponding 
pressure,  in  pounds  per  square  foot;  and  since  ventilating 
pressure  (Ib.  per  sq.  ft.)  is  the  difference  of  pressure  between 
the  intake  and  return;  the  unit  pressure  p,  in  any  given 
case,  is  found  by  subtracting  the  weight  of  the  upcast-shaft 
column  from  that  of  the  downcast  column;  thus, 

Downcast-shaft  column,  Wd  =  /„„  _,      D 

Upcast-shaft  column,  wu  =    .'         ^D 

Uait  pressure,  p  =  1.3273 

which  can  be  written 

1.3273B  (T  --  t)  D 
P  "  (460+  T}  (460  +  0 


THEORY  OF  VENTILATION  169 

Calculation  of  Air  Column. — The  air  column  corresponding 
to  the  above  unit  ventilating  pressure  can  be  expressed  in 
terms  of  either  the  downcast  or  upcast  air.  The  air  in  the 
downcast  being  heavier  than  that  in  the  upcast,  gives  a 
shorter  air  column  for  the  same  pressure. 

To  find  the  air  column  (hd)  in  terms  of  the  downcast  air, 
divide  the  above  expression  for  unit  ventilating  pressure  by  the 
weight  (wd)  of  1  cu.  ft.  of  downcast  air  (temp.  =  t),  which  gives 

/,         P_    =(T  -t)D 
Wd  -  460  +  T 

To  find  the  corresponding  air  column  (hu)  in  terms  of  the 
upcast  air,  divide  the  same  expression  for  unit  ventilating 
pressure  by  the  weight  of  1  cu.  ft.  of  upcast  air  (temp.  =  T), 
which  gives 

p      (T  -  t)  D 
wu       460  +  t 

Effective  Depth  of  Air  Column. — It  has  been  shown  that  in 
all  shaft  ventilation  the  effective  "head  of  air  column"  D 
is  the  difference  in  elevation  of  the  top  of  the  upcast  and  the 
bottom  of  the  downcast.  This  applies  equally  to  all  forms 
of  natural,  furnace  or  fan  ventilation,  in  shaft  mines,  where 
a  positive  or  negative  air  column  may  exist. 

Likewise,  in  drift  or  slope  mines,  the  same  law  will  apply, 
except  where  a  long  slope  causes  an  appreciable  rise  in  the 
temperature  of  the  downcast  air;  and  in  the  furnace  ventila- 
tion of  a  slope  mine.  In  either  of  these  two  cases,  three  tem- 
peratures may  be  concerned:  (1)  average  upcast  temperature 
in  the  shaft;  (2)  average  downcast  temperature  in  the  slope; 
(3)  outside  temperature. 

In  furnace  ventilation,  in  inclined  seams,  also,  three  tem- 
peratures must  be  considered:  (1)  average  temperature  of  the 
furnace  (upcast)  shaft;  (2)  mine  temperature,  rise  or  dip  of 
seam;  (3)  average  downcast  temperature.  In  a  few  cases,  a 
fourth  (4)  outside  temperature  may  require  consideration.  In 
all  cases  where  more  than  two  temperatures  are  concerned 
it  is  necessary  to  calculate  the  column  for  each  separate  tem- 
perature and  corresponding  depth  and  take  their  algebraic  sum. 


170  MINE  GASES  AND  VENTILATION 

In  practice,  the  arrangement  of  the  circulation  in  the  mine 
may  be  such  that  the  rise  or  dip  column  is  eliminated  by  a 
balance  of  intake  and  return  columns  of  equal  temperature. 

PROBLEMS 

Example.  —  A  shaft  mine,  in  a  level  seam,  is  ventilated  by  a  furnace. 
The  furnace  shaft  is  900  ft.  deep  and  has  an  average  temperature  of 
300  deg.  F.  ;  the  downcast  shaft  is  600  ft.  deep.  Calculate  the  air  column 
producing  circulation  in  this  mine  and  the  corresponding  ventilating 
pressure  and  water  gage  when  the  temperature  of  the  outside  air  is  20 
deg.  F.  and  the  barometer  30  in. 

Solution.  —  The  effective  head  of  air,  in  this  case,  is  D  =  900  ft.  and, 
assuming  that  the  temperature  of  the  downcast  shaft  is  practically  the 
•same  as  that  of  the  outside  air,  which  is  commonly  true,  the  air  column, 
expressed  in  terms  of  the  downcast  air,  is 

(T  -  t)D  =  (300  -  20)  900      280  X  900 
d       460  +  T          460  +  300  760 

Expressed  in  terms  of  the  upcast  air  the  air  column,  in  this  mine,  is 
_  (T  -  t)D  _  (300  -  20)  900  _  280  X  900 
"  ' 


460  +t    '         460  +20  480 

The  pressure  is  found  by  multiplying  either  of  these  air  columns  by  the 
corresponding  weight  of  downcast  or  upcast  air. 


Thus  (downcast),  p  =  -       ~i~  X  331.5  =  27.5  Ib.  per  sq.  ft. 

4oO  "|"  ^0 


i 
Or  (upcast),  p  =  +  X  525  -  27.5  Ib.  per  sq.  ft. 

The  corresponding  water  gage  is,  then, 

w.g.  =  27.5  -5-  5.2  =  5.3  in.,  nearly 

Example.  —  A  slope  mine  is  ventilated  by  means  of  a  blowing  or  force 
fan  located  at  the  top  of  an  air  shaft  800  ft.  deep.  The  slope  is  the  main 
return  airway  and  the  elevation  at  its  mouth  is  275  ft.  below  that  of  the 
top  of  the  air  shaft.  What  natural  air  column  exists,  assuming  the  tem- 
perature of  the  mine  is  60  deg.  and  that  of  the  outside  air  10  deg.  below 
zero  (•—  10°F.);  and  is  this  positive  or  negative? 

Solution.  —  The  effective  head  of  air,  in  this  case,  is  D  =  800  —  275  = 
525  ft.;  because  the  downcast  fan  shaft  has  the  same  temperature  as 
the  outside  air  column,  which  therefore  balances  275  ft.  of  the  shaft 
column.  The  downcast  air  in  the  shaft  being  colder  and  heavier  than 
the  upcast  or  return  air  in  the  slope,  the  resulting  air  column  assists  the 
circulation  produced  by  the  fan  and  is,  therefore,  a  positive  air  column. 
It  is 

j,     _  [60  -(-10)]X525  _  (60  +  10)  525  _  70  X  525 

hd  ~  460  +  60  520  520 


THEOR  Y  OF  YEN  TIL  A  TION  171 

This  air  column  is  in  terms  of  the  downcast  air,  which  weighs,  assum- 
ing a  barometric  pressure  B  =  30  in., 

1.3273  X  30       39.819 
Wd  =  460  +  (-10)  =  "450- 

The  natural  pressure  due  to  this  air  column  is  then 

pn  =  70.67  X  0.0885  =  6.25  Ib.  per  sq.  ft. 

Ques.  —  If  the  fan,  in  this  example,  were  to  be  reversed  so  as  to  exhaust 
air  from  the  mine,  thereby  making  the  slope  the  intake  and  the  fan  shaft 
the  upcast,  what  air  column  would  result,  if  the  average  slope  tem- 
perature is  then  40°  F.? 

Arts.  —  In  this  case,  three  air  columns  exist,  two  assisting  and  one 
opposing  the  circulation  induced  by  the  fan.  They  are  as  follows: 

1.3273  X  30  . 


Outside  column  (positive),  w0  = 


~~"    JLU 


1.3273  X  30  v 
Slope  column  (positive),  w,  =          „         ~     X  525 

1   ^97*?   V  ^0 

Shaft  column  (negative),  wu  =     46Q  +  ^0      X  800 

The  net  air  column,  expressed  in  terms  of,  say  the  slope  air,  is  now 
found  by  dividing  the  algebraic  sum  of  these  positive  (+)  and  negative 
(  —  )  columns  by  the  weight  of  1  cu.  ft.  of  the  slope  air,  which  gives  after 
simplifying, 

,         ,,AA   ,  A.         275  525  800 

A.  =  (460  +4 


/275  .   525      800\ 
1450  +  500  ~  520J 


The  weight  of  1  cu.  ft.  of  slope  air  is 

1.3273  X  30      39.819 
460+40         "SOOT  : 

The  natural  pressure  assisting  the  circulation  is  then 
pn  =  61.3  X  0.0796  =  4.88  Ib.  per  sq.  ft. 

Example.  —  To  show  the  effect  of  natural  air  columns  in  fan  ventila- 
tion, assume  a  shaft  mine  ventilated  by  means  of  a  fan;  the  seam  is 
practically  level  ;  the  fan  shaft  is  800  ft.  deep  and  the  hoisting  shaft  600 
ft.  deep. 

(a)  Assume  the  fan  is  exhausting  and  produces  a  circulation  of  200,000 
cu.  ft.  of  air  against  a  water  gage  of  2  in.,  in  the  winter  when  the  outside 
temperature  is  30  deg.  and  that  of  the  mine  60  deg.  F.,  and  calculate  the 
resulting  water  gage  and  the  volume  of  air  that  the  fan  will  circulate, 
running  at  the  same  speed  in  the  summer  season  when  the  outside  tem- 
perature is  70  deg..  and  that  of  the  mine,  as  before,  60  deg.  F. 

(6)  Assume  the  same  conditions  in  the  mine  and  the  same  respective 
temperatures  and  calculate  the  water  gage  and  volume  of  air  this  fan  will 


172  MINE  GASES  AND  VENTILATION 

produce  when  running  at  the  same  speed  and  blowing  instead  of  ex- 
hausting the  air,  for  the  winter  and  summer  seasons,  respectively. 

Solution. — (a)  When  the  fan  is  exhausting,  the  fan  shaft  being  the 
upcast,  the  effective  depth  of  air  column  is  D  =  800  ft.  The  natural 
water  gage  due  to  this  depth  (barom.,  B.  =  30  in.)  is 

1.3273  X  30(60  -  30)800 
Winter,         w.g.n  -  (460  +  eo)  (460  +  30)5.2  =  °'72  in' 

1.3273  X  30(70  -  60)800 
Summer,      w.g.n  =  (4qo  +  70)  (460  +  60)6.2  =  °'22  m' 

In  the  circulation  of  200,000  cu.  ft.  of  air,  under  a  2-in.  water  gage, 
as  stated  in  the  question,  therefore,  the  water  gage  due  to  the  action  of 
the  fan  is  2  —  0.72  =  1.28  in.,  the  natural  water  gage,  in  this  case, 
assisting  circulation,  being  positive.  In  the  summer  season,  the  fan 
exhausting  at  the  same  speed  as  before  will  create  the  same  ventilating 
pressure  and  water  gage  (1.28  in.) ;  but,  the  natural  air  column  now  being 
negative  (0.22  in.),  the  effective  water  gage  producing  circulation  is 
1.28  —  0.22  =  1.06  in.  Then,  since  the  circulation  in  any  given  mine 
or  airway  varies  as  the  square  root  of  the  pressure  or  water  gage,  the 
quantity  ratio  is  equal  to  the  square  root  of  the  water-gage  ratio. 


200,000 
Summer  (exhausting),  x  =  200,000  X  0.728  =  145,600  cu.  ft.  per  min. 

(b)  When  the  fan  is  blowing  the  hoisting  shaft  is  the  upcast  and  the 
effective  depth  of  air  column  is  then  D  =  600  ft.  The  natural  water 
gage  is  then  600/800  =  ^  of  the  value  previously  found;  or  %  X  0.72  = 
0.54  in.  (winter),  and  %  X  0.22  =  0.165  in.  (summer).  As  before,  the 
natural  gage  is  positive  in  winter  and  negative  in  summer,  which  makes 
the  effective  gage  1.28  +  0.54  =  1.82  in.  (winter)  and  1.28  —  0.165  = 
1.115  in.  (summer).  The  circulation  is  then 

/I    00 

Winter  (blowing),         x  =  200,000-^^-  =  say  190,800  cu.  ft.  per  min. 


Summer  (blowing),       x  =  200, 000 -y~     =  say  149,400  cu.  ft.  per  min. 

FLOW  OF  AIR  IN  AIRWAYS 

The  flow  of  air  in  a  conduit  or  airway  is  in  obedience  to 
an  excess  of  pressure  at  one  end  of  the  conduit  over  that  at 
the  other  end.  Air  always  moves  from  a  point  of  higher  pres- 
sure toward  a  point  of  lower  pressure.  The  moving  air  is 
called  the  air  current. 


THEORY  OF  VENTILATION  173 

Velocity  of  Air  Currents. — The  rate  of  motion  or  the  dis- 
tance traveled  per  unit  of  time  is  called  the  velocity  of  the 
air  current.  The  velocity  is  commonly  expressed  in  feet  per 
second  or  feet  per  minute,  as  most  convenient. 

Relation  of  Pressure  and  Velocity. — To  double  the  velocity 
of  air  in  an  airway  or  conduit  requires  four  times  the  pres- 
sure; and  since  2  =  \/4,  the  velocity  v  varies  as  the  square 
root  of  the  pressure  p\  thus 

v  varies  as  \/p 
or,  vice  versa, 

p  varies  as  t>2 

For  example,  if  an  airway  in  a  mine  is  of  such  size  and 
length  that  the  pressure  per  square  foot  at  the  intake  is  3  Ib. 
greater  than  that  at  the  discharge  opening,  and  this  difference 
of  pressure  produces  a  velocity  of  5000  ft.  per  min.;  it  will 
require  a  difference  of  pressure  of  4  X  3  =  12  Ib.  per  sq.  ft. 
to  produce  a  velocity  of  1000  ft.  per  min.  in  the  same  airway. 

Solution  by  Ratios. — -Expressed  as  ratios,  the  solution  is 
always  simpler  and  shorter,  because  the  method  admits  of 
ready  cancellation,  thereby  keeping  the  numbers  small  and 
reducing  the  amount  of  necessary  work.  For  example,  when 
quantities  are  proportional  their  ratios  are  equal.  Or,  in  this 
case,  the  velocity  ratio  is  equal  to  the  square  root  of  the 
pressure  ratio.  Calling  the  first  velocity  v\,  second  velocity 
Vz',  the  first  pressure  p\  and  the  second  pressure  p2,  we  have 

v*  _     fpt 

1)\ 

or,  vice   versa, 


Example. — What  difference  of  pressure  per  square  foot  will  be  required 
to  produce  a  velocity  of  1200  ft.  per  min.  in  an  airway  where  the  air  is 
moving  at  the  rate  of  500  ft.  per  min.,  under  a  moving  pressure  of  3.5 
Ib.  per  sq.  ft.? 

Solution. — Let  x  =  the  required  difference  of  pressure;  then 
x          /1200\2        /12\2        144 
3^  =  (  5007      "  V*7       =   25T  =  5'76 
x  =  3.5  X  5.76  =  20.16  Ib.  per  sq.  ft. 


174  MINE  GASES  AND  VENTILA  TION 

Example.  —  If  a  difference  of  pressure  between  the  two  ends  of  an  air- 
way, of  8  Ib.  per  sq.  ft.,  produces  a  velocity  of  600  ft.  per  min.,  what 
will  be  the  velocity  in  the  same  airway  when  the  difference  of  pressure 
is  only  2  Ib  per  sq.  ft.? 

Solution.  —  In  this  case,  calling  the  required  velocity  x, 


JL   _  J2  _  Ji  _  1 

600         \8         \4  ~  2 

x  =  600  X  H  =300  ft.  per  min. 


VENTILATING  PRESSURE 

Pressure  Producing  Circulation. — In  mine  ventilation,  the 
term  ''ventilating  pressure"  is  the  pressure  exerted  to  move 
the  air.  It  is  the  difference  between  the  intake  pressure  and 
the  discharge  pressure.  Since  the  pressure  of  the  atmosphere 
is  equal  at  both  ends  of  the  airway  it  may  be  disregarded, 
as  far  as  the  movement  of  the  air  is  concerned. 

The  Blowing  System  of  Ventilation. — To  move  the  air  or 
cause  it  to  circulate  in  an  airway  or  a  mine,  an  extra  pres- 
sure must  be  created  at  one  end  of  the  airway,  so  as  to  over- 
come the  resistance  of  the  mine  due  to  friction.  This  is 
called  the  "blowing"  system  of  ventilation,  because  the  air 
is  blown  through  the  airway  by  the  pressure  created. 

The  Exhaust  System  of  Ventilation. — The  same  difference 
of  pressure  may  be  caused  by  decreasing  the  atmospheric 
pressure  at  one  end  of  the  airway,  when  the  full  pressure 
of  the  atmosphere  at  the  other  end  will  cause  the  air  to  move 
toward  the  point  where  the  pressure  is  less.  The  principle 
is  that  commonly  called  " suction;"  but  this  system  is  known 
HS  the  "exhaust"  system  of  ventilation. 

How  Pressure  is  Produced. — Various  means  have  been  used 
to  cause  a  circulation  of  air  in  mine  airways.  The  wind 
cowl,  waterfall  and  steam  jet  are  useful  under  favorable 
conditions  and  where  a  limited  air  supply  only  is  needed.  The 
mine  furnace,  built  in  the  mine  near  the  bottom  of  the  upcast 
shaft,  is  often  used  in  n  on  gaseous  mines,  especially  in  deep 
shafts  (see  Furnace  Ventilation).  The  most  reliable  means 
of  creating  pressure  in  mine  ventilation,  however,  is  the  mine 
fan,  which  is  generally  erected  at  the  surface,  either  at  the 


THEOR  Y  OF  YEN  TIL  A  TION  175 

top  of  the  downcast  shaft,  as  a  blower;  or  at  the  top  of  the 
upcast,  as  an  exhaust  fan  (see  Fan  Ventilation).  The  blow- 
ing fan  creates  a  pressure  above  that  of  the  atmosphere,  while 
the  exhaust  fan  reduces  the  atmospheric  pressure. 

How  Pressure  is  Estimated. — In  mine  ventilation,  the 
pressure  producing  circulation  is  estimated  in  height  of  air 
column,  as  in  natural  ventilation  and  often  in  furnace  ven- 
tilation. The  more  common  method,  however,  is  to  state  the 
pressure  in  pounds  per  square  foot  or  ounces  per  square  inch. 
Pressure  is  also  stated  in  inches  of  water  gage.  These  all  refer 
to  the  unit  of  ventilating  pressure  or  simply  "unit  pressure." 

Atmospheric  pressure  is  given  in  pounds  per  square  inch, 
or,  as  barometric  pressure  (which  is  the  same  as  atmospheric 
pressure),  in  inches  of  mercury. 

1  in.  water  gage  =  5.2  Ib.  per  sq.  ft. 
1  in.  mercury       =  0.491  Ib.  per  sq.  in. 
1  oz.  per  sq.  in.    =9  Ib.  per  sq.  ft. 
1  in.  mercury       =  13.6  in.  water  gage 

How  Pressure  is  Measured. — In  mine  ventilation,  the  pres- 
sure producing  circulation  is  commonly  measured  by  means 
of  the  water  gage;  or,  in  case  of  high  pressures  a  special  form 
of  manometer  is  sometimes  used.  The  manometer  differs  from 
the  water  gage  in  having  one  end  of  the  bent  tube  closed  so 
that  the  rise  of  the  water  level  in  that  arm  of  the  tube  com- 
presses the  air  above  the  water,  which  lessens  the  rise  of 
water  level  and  gives  a  greater  range  of  readings. 

The  Mine  Water  Gage. — This  consists  of  a  glass  tube  of 
about  %-in.  bore,  bent  to  the  shape  of  the  letter  U  and 
mounted  on  a  solid  base.  Three  styles  of  water  gage  are 
shown  in  Fig.  24.  These  differ  only  in  the  kind  of  scale.  The 
first  two  on  the  left  have  the  zero  at  the  center  of  the  scale  and 
read  up  and  down  to  the  respective  water  levels.  The  first 
of  these  scales  is  graduated  to  full-length  inches,  and  to  obtain 
a  correct  reading  it  is  necessary  to  add  the  two  readings  to- 
gether, or  double  either  of  them,  as  they  are  equal.  To  avoid 
this  necessity  the  second  scale  is  made  of  half-length  inches,  so 
that  either  the  upper  or  the  lower  reading  gives  the  full  gage 


176 


MINE  GASES  AND  VENTILATION 


required,  which,  in  this  case,  is  3  inches.  As  shown  in  the 
figure,  the  scale  is  adjustable  by  means  of  the  screw  rod  on 
which  it  is  mounted. 

When  the  zero  of  the  scale  is  at  the  middle  and  the  scale 
reads  up  and  down,  it  is  evident  that  the  scale  must  be  adjusted 
so  that  its  zero  will  correspond  with  the  two  water  levels,  before 
the  pressure  acts  on  the  gage.  When  the  pressure  acts  it 
depresses  the  water  level  in  one  arm  while  that  in  the  other 
arm  rises  an  equal  amount.  The  difference  between  these 
two  levels  is  the  actual  water  column  supported  by  the  differ- 


Fio.  24. 

ence  in  the  pressures  acting  on  the  water  in  the  two  arms.  As 
will  be  explained  later,  one  arm  of  the  gage  when  in  position 
is  open  to  the  intake  pressure  and  the  other  to  the  return. 
The  difference  between  these  two  pressures  is  the  pressure  that 
circulates  the  air  between  these  two  points. 

The  scale  shown  on  the  right  has  its  zero  at  the  bottom  and 
reads  upward.  This  scale  must  evidently  be  set,  after  the 
gage  is  in  position,  so  that  the  zero  will  correspond  with  the 
lower  water  level,  which  is  always  that  in  the  arm  open 
to  the  intake  pressure,  as  that  pressure  is  always  greater  than 
the  return  pressure.  The  reading  of  the  scale  at  the  upper 
level  is  then  the  required  gage. 

The  reading  of  each  of  the  three  gages  shown  in  the  figure 
is  3  in.,  which  indicates  a  ventilating  pressure  of  3  X  5.2 
=  15.6  Ib.  per  sq.  ft. 


THEORY  OF  VENTILATION 


177 


Reading  the  Water  Gage. — In  the  common  use  of  the  water 
gage,  in  mine  practice,  the  scale  is  not  read  closer  than  %  in. 
On  the  left  of  Fig.  25,  is  shown  a  portion  of  a  water  column 
and  scale  graduated  to  eighths  of  an  inch.  The  scales 
shown  in  Fig.  24  are  decimal  scales,  being  graduated  to 
tenths  of  an  inch  for  greater  accuracy.  In  all  engineering 
practice,  therefore,  and  whenever  accuracy  is  desired  the 
decimal  scale  shown  in  Fig.  24  is  used  and  the  reading  taken 
to  tenths  or  hundredths  of  an  inch. 

There  are  several  sources  of  possible  error  in  reading  the 
mine  gage.  If  the  gage  is  not  truly  vertical  the  reading  will 
not  be  correct.  Error  often  occurs  from  the  cupping  of  the 
surface  of  the  water  in  the  tube.  As  shown  in  Fig.  25,  the 


FIG.  25. 

reading  of  the  gage  should  be  taken  at  the  bottom  of  the  con- 
cave or  bowl.  This  will  give  greater  uniformity  in  the  results 
obtained. 

In  fan  ventilation,  especially  when  the  reading  is  taken 
in  the  fan  drift,  there  is  a  constant  oscillation  of  the  water 
level,  which  makes  it  difficult  to  decide  on  the  true  reading. 
The  oscillation  is  much  reduced  when  the  tube  of  the  gage  is 
contracted  at  the  bend.  The  best  gages  are  provided  with  a 
stop-cock  in  the  bend  by  which  the  connection  between  the 
two  arms  can  be  closed.  The  gage  can  then  be  carried  to  a 
more  convenient  place  to  be  read. 

Unit  of  Ventilating  Pressure. — In  mine  ventilation,  the 
unit  of  ventilating  pressure,  or  the  unit  pressure  producing  the 

circulation,   is  estimated  in  pounds  per  square  foot      This 
12 


1 78  MINE  GASES  AND  V  EN  TIL  A  TION 

is  calculated  from  the  reading  of  the  water  gage  by  multiply- 
ing that  reading,  in  inches,  by  5.2. 

On  the  right,  in  Fig.  25,  is  shown  clearly  how  the  constant 
5.2  is  derived.  The  weight  of  1  cu.  ft.  of  water  is,  practically, 
62.5  Ib.  The  figure  represents  a  cube  that  measures  12  in. 
on  each  edge;  the  base  of  the  cube  being  1  sq.  ft.  Since  the 
weight  of  12  in.  of  water,  resting  on  this  square  foot,  is  62.5 
Ib.,  the  weight  of  1  in.  of  water  covering  the  same  area  is  62.5 
-7-  12  =  5.2  Ib.,  which  represents  the  pressure,  in  pounds 
per  square  foot,  due  to  1  in.  of  water  column.  The  principle 
involved  is  that  the  unit  pressure  on  a  given  area  of  surface 
depends  only  on  the  height  of  water  column  the  pressure 
supports. 

The  Water  Gage  in  the  Mine. — As  used  in  the  mine,  the 
reading  of  the  water  gage  shows  the  difference  of  pressure 


FIG.  26. 

between  the  intake  and  return  airways,  at  the  point  where 
the  reading  is  taken.  The  intake  pressure  is  always  greater 
than  the  return  pressure  and  this  excess  or  difference  of  pres- 
sure is  what  moves  the  air  or  creates  the  current. 

The  use  of  the  instrument  is  clearly  illustrated  in  Fig.  26 
where  two  parallel  airways  are  shown  leading  into  the  mine, 
one  of  these  being  the  intake  and  the  other  the  return  airway 
of  that  section  of  the  mine.  It  makes  no  difference  on  which 
side  of  the  brattice  the  instrument  is  placed;  the  water  will 
always  be  depressed  in  that  arm  of  the  gage  which  is  open  to 
the  intake,  because  the  pressure  on  the  intake  is  always  greater 
than  that  on  the  return  airway. 

What  the  Water  Gage  Shows. — The  water-gage  reading  indi- 
cates the  ventilating  pressure  required  to  circulate  the  air, 


THEORY  OF  VENTILATION  179 

and  is  therefore  equal  to  the  resistance  of  the  airways  be- 
tween the  two  points  on  the  intake  and  the  return;  or,  in 
other  words,  the  resistance  inby  from  the  point  of  observa- 
tion. The  nearer  this  reading  is  taken  to  the  head  of  a  pair 
of  entries,  the  closer  it  will  approach  zero,  while  at  the  next 
to  the  last  crosscut  it  would  be  practically  zero. 

The  use  of  the  water  gage  in  mining  practice  is  of  great 
importance.  In  connection  with  the  observed  velocity  of  the 
air,  it  shows  the  " power  on  the  air"  or  the  power  producing 
the  circulation.  What  is  required  in  the  practical  ventilation 
of  a  mine  is  the  production  of  the  necessary  velocity  and 
volume  of  air,  with  the  smallest  expenditure  of  power.  The 
most  economical  circulation  is  obtained  when  the  required 
air  volume  is  circulated  by  the  least  power,  which  means  a 
comparatively  low  water  gage. 

The  circulation  of  a  comparatively  large  quantity  of  air 
under  a  low  gage  indicates  ideal  economic  conditions,  as  far 
as  the  circulation  is  concerned.  On  the  other  hand,  a  small 
air  volume  and  a  comparatively  high  water  gage  shows  a 
needless  waste  of  power.  In  practice,  an  unusual  reduction 
of  the  quantity  of  air  passing  in  a  mine  or  entry,  accompanied 
by  a  similarly  uncommon  rise  of  gage  pressure  would  indi- 
cate an  obstruction  of  the  airways. 

VELOCITY  OF  AIR  CURRENTS 

The  velocity  of  the  air  current  is  one  of  the  most  important 
factors  in  the  practice  of  mine  ventilation.  If  the  velocity  of 
the  air  current  is  too  low  the  ventilation  of  the  mine  is  ineffi- 
cient, as  the  air  will  not  sweep  away  the  accumulating  gases 
from  their  lurking  places  in  the  mine.  On  the  other  hand,  if 
the  air  moves  with  too  great  a  velocity,  not  only  do  the  work- 
men suffer  inconvenience,  but  the  high  velocity  of  the  current 
is  often  dangerous. 

Danger  of  High  Velocity. — A  rapid  air  current  carries  a 
great  quantity  of  dust,  and,  by  supplying  large  quantities  of 
oxygen,  maintains  an  unnecessarily  active  condition  of  the 
mine  atmosphere  that  favors  the  ignition  of  the  gas  and  dust. 
The  high  wind  creates  a  draft  that  greatly  intensifies  the 


180 


MINE  GASES  AND  VENTILATION 


flame  of  lamps  or  of  a  blast  of  powder  and  increases  the  pos- 
sibility of  ignition. 

How  Velocity  is  Estimated. — In  mine  ventilation  the  ve- 
locity of  the  ventilating  current  is  commonly  estimated  in 
feet  per  minute,  or  feet  per  second. 

How  Velocity  is  Measured. — A  simple  method  of  ascertain- 
ing, with  more  or  less  accuracy,  the  average  velocity  of  the 
air  current  passing  in  an  airway  is  to  measure  off  a  distance 
of,  say  300  ft.  along  a  straight  portion  of  the  airway;  and 


FIG.  27. 

note  the  exact  time  between  the  observed  flash  of  powder  at 
one  end  and  the  smell  of  smoke  at  the  other  end  of  this  dis- 
tance. The  distance  (300  ft.)  divided  by  the  time  will  give 
the  velocity  of  the  air  in  the  center  of  the  entry.  The  average 
velocity  of  the  current  may  then  be  taken  as  ££  of  this  observed 
velocity.  For  example,  if  the  observed  time  is  30  sec.,  the 
center  velocity  is  300  -5-  30  =  10  ft.  per  sec.;  and  the  average 
velocity  %  x  10  =  8  ft.  per  sec.  or  8  X  60  =  480  ft.  per  min. 

The  Anemometer. — The  common  method  of  measuring  the 
velocity  of  the  air  in  airways  is  by  the  use  of  the  anemometer, 
one  form  of  which  is  shown  in  Fig.  27.  The  dial  hands  record 


THEORY  OF  VENTILATION  181 

the  number  of  revolutions  of  the  vane.  The  instrument  is  so 
calibrated  that  each  revolution  of  the  vane  corresponds  to 
1  ft.  of  air  travel.  The  reading  of  the  dial,  therefore,  shows  the 
distance  the  air  traveled  during  the  time  that  the  instrument 
was  exposed  to  the  current.  Hence,  this  reading  divided  by 
the  time  of  exposure,  in  minutes,  will  give  the  velocity  of  the 
current  in  feet  per  minute.  A  single  revolution  of  the  large 
hand  corresponds  to  100  revolutions  of  the  vane.  The  small 
dials  register  the  total  reading. 

QUANTITY  OF  AIR 

The  term  "  quantity,"  in  mine  ventilation,  refers  to  the 
volume  of  air  passing  in  an  airway,  estimated  in  cubic  feet 
per  minute.  This  is  often  spoken  of  as  the  "circulation"  of 
the  airway  or  mine. 

How  Quantity  is  Estimated. — As  stated  above,  the  quan- 
tity of  air  circulated  in  an  airway  or  mine,  or  the  "circula- 
tion," as  it  is  called,  is  always  estimated,  in  this  country,  in 
cubic  feet  per  minute. 

How  Quantity  is  Measured. — To  measure  the  quantity,  in 
ventilation,  it  is  necessary  (1)  to  measure  the  sectional  area 
of  the  airway  at  the  point  of  observation  and  (2)  to  care- 
fully measure  the  average  velocity  of  the  air  current  at  the 
same  point.  From  these  measurements,  the  volume  of  air 
passing  or  the  circulation  is  calculated  by  means  of  the 
formula, 

Quantity  =  area  X  velocity 
q  —  av 

Example. — Calculate  the  circulation  in  an  airway  having  a  sectional 
area  of  50  sq.  ft.,  the  average  velocity  of  the  air  current  being  600  ft. 
per  min. 

Solution. — Substituting  the  given  values  in  the  formula  for  quantity 
in  terms  of  velocity  and  area, 

q  =  av  =  50  X  600  =  30,000  CM.  ft.  per  min. 

Quantity  of  Air  Required. — In  determining  the  required  cir- 
culation of  a  mine,  it  is  necessary  to  consider  (1)  the  re- 
quirements of  the  mining  law  of  the  state  in  which  the  mine 


182  MINE  GASES  AND  VENTILATION 

is  located  and  (2)  the  requirements  of  the  mine  as  determined 
by  the  natural  conditions  existing  in  the  seam  and  the  en- 
folding strata. 

Requirements  of  the  Mining  Law. — These  vary  somewhat 
in  different  states.  Owing  to  the  numerous  and  changing 
conditions,  in  mines,  mining  laws  are  of  necessity  arbitrary 
standards,  which  must,  however,  be  met,  except  in  cases 
where  the  law  specially  confers  discretionary  powers  upon  the 
mine  inspector  or  the  mine  foreman,  thereby  authorizing  them 
to  decrease  the  circulation  in  any  mine  or  section  of  the  mine, 
as  conditions  may  require  or  their  judgment  dictate. 

The  mining  law  commonly  specifies  from  100  to  150  cu.  ft. 
per  man,  per  min.,  for  nongaseous,  and  200  cu.  ft.  per  min.,  for 
gaseous  mines.  In  addition,  some  of  the  laws  require  from 
500  to  600  cu.  ft.  per  min,,  for  each  animal  employed 
underground. 

Natural  Requirements. — Gaseous  mines  naturally  require 
more  air  than  nongaseous  mines.  The  rise  workings  of  seams 
generating  marsh  gas  or  the  dip  workings  of  mines  giving 
off  quantities  of  blackdamp  are  often  difficult  to  ventilate  and 
require  a  circulation  greater  than  what  the  law  specifies,  in 
order  to  keep  the  workings  free  from  gas  and  healthful  and 
safe  for  work.  Slips  and  faults  often  give  off  much  gas  when 
least  expected  and  require,  therefore,  a  larger  circulation  of 
air  than  would  otherwise  be  necessary  in  the  same  mine. 

WORK  OR  "  POWER  ON  THE  AIR" 

The  terms  "work"  and  "power"  as  used  in  mine  ventila- 
tion, are  synonymous,  because  the  work  performed  in  moving 
the  air  through  the  mine  airways  is  based  on  a  unit  of  time, 
both  the  velocity  and  the  quantity  being  rated  per  minute  of 
time. 

Power  on  the  Air. — The  air  current  in  an  airway  or  mine 
is  moved  by  a  pressure  called  the  "ventilating  pressure." 
The  ventilating  pressure  or  the  pressure  producing  the  cir- 
culation is  the  total  pressure  pa  exerted  on  the  entire  sec- 
tional area  of  the  airway,  as  illustrated  in  Fig.  28.  The  small 


THEOR  Y  OF  V  EN  TIL  A  TIOK  1 83 

arrowheads  in  the  figure  represent  the  unit  pressure  or  the 
pressure  p  on  each  square  foot  of  cross-section.  The  large 
arrow  shown  at  A  represents  the  total  pressure  P  =  pa. 

It  is  a  law  of  mechanics  that  when  a  force  pa  moves  or  is 
exerted  through  a  distance  v  the  work  performed  is  equal  to 
the  product  pav  of  the  force  and  the  distance.  But  in  this 
case,  the  force  pa  moves  through  the  distance  v  in  one 
minute.  The  work  (pav)  is,  therefore,  performed  in  one 
minute  and  is  the  "  power  on  the  air."  The  work  performed 
per  minute  or  the  power  on  the  air  is  expressed  in  foot-pounds 


FIG.  28. 

per  minute.     Calling  this  work  per  minute  or  power  on  the  air 
u,  the  formula  for  power  is 

Power  =  unitpres.  X  area  X  vel. 

u  =  pav 

Again,    since   q  =  av,    the  formula  for  power  on  the  air 
may  be  written: 

Power  =  quantity  X  unit  pres. 

u  =  qp 

The  formula  for  horsepower  of  the  circulation  is,  there- 
fore, since  1  hp.  =  33,000  ft.-lb.  per  min. 

qp 


H 


33,000 


184  MINE  GASES  AND  VENTILATION 

The  power  formulas,  in  ventilation,  make  it  possible  to 
calculate  the  power  required  to  produce  any  given  circula- 
tion, against  any  given  pressure  or  water  gage  when  the 
efficiency  of  the  venilator  is  known  or  assumed. 

EQUIVALENTS  IN  MEASUREMENT 

Air  Column  and  Water  Gage. — Since  water  is  practically 
815  times  as  heavy  as  air  at  normal  temperature  and  pres- 
sure, 1  ft.  of  water  column  measures  the  same  pressure  as 
815  ft.  of  ordinary  air  column;  and  1  in.  of  water  gage  is  there- 
fore equal  to  815  -f-  12  =  say  68  ft.  of  air  column,  which 
gives  the  following: 

Rule. — -To  reduce  feet  of  air  column  to  inches  of  water 
gage,  divide  by  68. 

To  reduce  inches  of  water  gage  to  feet  of  air  column,  mul- 
tiply by  68. 

Air  Column  and  Unit  Ventilating  Pressure.— Since  air  at 
a  normal  temperature  and  pressure  weighs,  practically,  13 
cu.  ft.  to  the  pound,  every  13  ft.  of  air  column  represents,  ap- 
proximately, a  ventilating  pressure  of  1  Ib.  per  sq.  ft.,  which 
gives  the  following: 

Rule. — To  reduce  feet  of  air  column  to  'unit  pressure,  di- 
vide by  13. 

To  reduce  unit  pressure  (Ib.  per  sq.  ft.)  to  feet  of  air  col- 
umn, multiply  by  13. 

Air  Column  and  Barometric  Pressure. — Since  1  cu.  in.  of 
mercury  weighs  0.491  Ib.,  each  inch  of  mercury  column  indi- 
cates a  pressure  of  0.491  Ib.  per  sq.  in.;  0.491  X  144  =  70.7 
Ib.  per  sq.  ft.;  and  since  each  pound  per  square  foot  of  pres- 
sure corresponds  to  13  ft.  of  air  column,  approximately,  1  in. 
of  barometer  =  70.7  X  13  =  say  920  ft.  of  air  column,  which 
gives  the  following: 

Rule  (Approximate). — To  reduce  feet  of  air  column  to 
inches  of  barometer,  divide  by  920. 

To  reduce  barometric  pressure  (inches)  to  feet  of  air  column, 
multiply  by  920. 

Barometric  and  Unit  Ventilating  Pressure. — Barometric 
pressure  is  always  expressed  in  inches  of  mercury  column. 


THEORY  OF  VENTILATION 


185 


Unit  ventilating  pressure  is  expressed  in  pounds  per  square 
foot,  ounces  per  square  inch,  or  inches  of  water  gage. 

Rule. — To  reduce  barometric  pressure  (inches)  to  ventilat- 
ing pressure  (Ib.  per  sq.  ft.),  multiply  by  70.7;  or  to  ventilat- 
ing pressure  (oz.  per  sq.  in.),  multiply  by  0.491  X  16  =  7.856; 
or  to  water  gage  (in.),  multiply  by  70.7  -f-  5.2  =  13.6,  which 
is  the  specific  gravity  of  mercury  referred  to  water  as  a 
standard. 

Since  13  ft.  air  column  represents  a  pressure  of  1  Ib.  per 
sq.  ft.,  a  pressure  of  1  oz.  per  sq.  in.  corresponds  to  an  air 
column  of  (13  X  144)  -s-  16  =  117  ft. 

EQUIVALENTS  IN  PRESSURE 

VOLUME  OR   QUANTITY  or  AIR  IN  CIRCULATION  (cu  rr  PER  HIM) 


£  60 

$  so 

£  40 

?  M 


5 

f> 

4* 


--MO 

r25.0" 

=         t 

*"! 

15.0  3 

g 

*.j 


FIG.  29. 


Air  column  (ft.) 

Pressure  (Ib.  per  sq.  ft.) 
Pressure  (oz.  per  sq*  in.) 
Water  gage  (in.) 


=      68 


uo  X  water  gage  (in.); 

13  X  pressure  (Ib.  per  sq.  ft.); 

117  X  pressure  (oz.  per  sq.  in.)  ; 

920  X  barometric  pressure  (in.); 

5.2  X  water  gage  (in.); 

70.7.  X  barometric  pressure  (in.); 

0.58  X  water  gage  (in.); 

7.86  X  barometric  pressure  (in.); 

13.6  X  barometric  pressure  (in.). 


Power- Volume -Pressure   Diagram. — The   diagram   shown 
in  Fig.  29  is  convenient  as  showing  at  a  glance  the  power  re- 


186  MINE  GASES  AND  VENTILATION 

quired  to  circulate  a  given  quantity  of  air  against  a  certain 
pressure,  in  pounds  per  square  foot,  ounces  per  square  inch,  cl- 
inches of  water  gage.  In  order  to  find  the  power  required  to 
pass  any  given  volume  of  air  against  any  given  pressure  or 
water  gage,  follow  the  diagonal  line  corresponding  to  the  given 
water  gage  to  its  intersection  with  the  vertical  line  corre- 
sponding to  the  given  volume  and  read  this  point  of  intersec- 
tion on  the  power  scale  at  the  left  of  the  diagram. 

For  example,  it  requires  50  hp.  to  pass  80,000  cu.  ft.  of  air 
per  minute,  under  a  4-inch  water  gage  or,  reversing  the  order, 
30  hp.  will  pass  about  96,000  cu.  ft.  per  minute  under  a  2-inch 
gage.  Since  the  power  is  proportional  to  the  quantity  and 
pressure  alike,  in  order  to  deal  with  higher  values  than  those 
given  in  the  diagram,  it  is  only  necessary  to  treat  these  as 
multiples  of  the  values  given  in  the  diagram.  Thus,  100  hp 
would  pass  160,000  cu.  ft.  under  a  4-inch  gage;  or  320,000  cu. 
ft.  under  a  2-inch  gage.  The  horsepower  in  this  diagram  is 
the  power  on  the  air,  which  is  commonly,  in  fan  practice,  60 
per  cent,  of  the  horsepower  of  the  engine  or  the  indicated 
horsepower. 

EXAMPLES  FOR  PRACTICE 

1.  How  many  feet  of  air  column  is  equivalent  to  a  mine  water  gage 
of  three  inches? 

Solution. — Under  ordinary  or  normal  conditions  water  weighs   815 
times  as  heavy  as  the  same  volume  of  air;  hence, 

1  ft.  (12  in.)  water  column  =  815  ft.  air  column 
1  in.  water  gage  =  815  -r-  12  =  68  ft.  air  column 
3  in.  water  gage  =  3  X  68  =  204  ft.  air  column 

2.  Express  the  pressure  equivalent  to  200  ft.  of  ordinary  air  column, 
in  pounds  per  square  ft.;  ounces  per  square  inch;  inches  of  barometer; 
inches  of  water  gage. 

Solution. — 

200  -=-  13  =  15.39  Ib.  per  sq.  ft.,  nearly 
200  -=-117=  1.71  02.  per  sq.  in.,  nearly 
200  -f-  920  =  0.22  in.  of  mercury,  nearly 
200  -5-  68  =  2.94  in.  of  water  gage. 

3.  What  is  the  pressure  of  the  atmosphere,  in  pounds  per  square  inch, 
corresponding  to  a  barometric  pressure  of  30  in.? 


THEORY  OF  VENTILATION  187 

Solution. — 

30  X  7.86  =  235.8  oz.  per  sq.  in. 
235.8  -T-  16  =  14.74  Ib.  per  sq.  in.,  nearly 

4.  Find  the  pressure  in  ounces  per   square  inch  corresponding  to  a 
water  gage  of  2.5  in. 

Solution. — 

2.5  X  0.58  =  1.45  oz.  per  sq.  in. 

5.  Find  the  barometric  pressure  in  inches  of  mercury  corresponding 
to  a  water  gage  of  3.4  in. 

Solution. — 

3.4  +  13.6  =  0.25  in. 

6.  If  an  aneroid  barometer  gives  a  reading  of  29.65  in.  on  the  surface, 
what  should  be  the  reading  at  the  bottom  of  a  downcast  shaft  500  ft. 
deep  where  the  ventilating  pressure  caused  by  a  blowing  fan  gives   a 
water  gage  of  2.85  in.,  assuming  all  readings  are  taken  at  about  the  same 
time? 

Solution. — The  air  column  in  this  shaft  will  increase  the  barometric 
pressure  500  -5-  920  =  0.54  in.  The  water  gage  due  to  the  blower  will 
still  further  increase  the  barometric  pressure,  at  the  foot  of  the  downcast 
shaft,  2.85  -5-  13.6  =  0.21  in.  The  reading  of  the  aneroid,  therefore, 
should  be  29.65  +  0.54  +  0.21  =  30.4  in.,  approximately. 

7.  In  a  mine  ventilated  by  an  exhaust  fan,  giving  a  water  gage  of  2.33 
in.,  if  aneroid  readings  taken  on  the  surface  and  at  the  bottom  of  the 
upcast  shaft  show  a  difference  of  0.77  in.,  what  is  the  calculated  depth  of 
the  shaft? 

Solution. — The  action  of  the  exhaust  fan  makes  the  aneroid  reading 
at  the  shaft  bottom  lower  than  it  would  be  if  the  fan  were  not  running, 
and  decreases  the  difference  of  the  surface  and  underground  readings 
2.33  -T-  13.6  =  0.17  in.  of  mercury.  The  difference  of  reading  due  to 
the  depth  of  the  shaft  only  is,  therefore,  0.77  +  0.17  =  0.94  in.  of 
mercury.  Reducing  this  barometric  difference  to  air  column  gives  for 
the  approximate  depth  of  the  shaft  920  X  0.94  =  say  865  ft.  under 
ordinary  conditions. 

MINE  AIRWAYS 

Definition  of  Terms. — The  term  "airway,"  in  mining,  gen- 
erally relates  to  a  passageway  for  the  circulation  of  the  air 
current,  in  distinction  from  a  haulage  road  or  travelingway, 
although  these  entries  may  serve  also  as  airways.  The  entry 
by  which  the  air  current  enters  the  mine  is  called  the  main 
'•'intake,"  and  that  by  which  it  is  carried  out,  the  main  "re- 
turn." In  like  manner,  the  two  shaft  or  slope  openings  in 


1 88  MINE  GASES  AND  YEN  TIL  A  TION 

a  mine  are  called,  respectively,  the  "downcast"  and  the 
"upcast." 

The  "  perimeter  "of  an  airway  is  the  distance  measured 
around  the  circumference  of  its  cross-section.  The  "area" 
or  " sectional  area"  of  an  airway  is  the  area  of  its  cross- 
section. 

The  " rubbing  surface"  s  of  an  airway  is  the  entire  inner 
surface  of  the  same;  and  is  found  by  multiplying  the  perim- 
eter o  by  the  length  /,  of  the  airway;  thus, 

s  =  lo 

Essential  Features  of  Mine  Airways. — Airways  in  mines 
should  be  as  straight  as  possible  and  avoid  all  sharp  bends 
and  other  obstructions  that  increase  the  resistance  of  the 
airway  to  the  flow  of  air.  The  shape  of  the  airway  is  im- 
portant as  affecting  the  pressure  required  to  pass  a  given 
quantity  of  air. 

Shape  of  Airways. — The  cross-section  of  an  airway  may  be 
a  circle,  square,  rectangle,  ellipse,  or  any  combination  of  these 
that  best  meets  the  needs  or  conditions.  For  the  purpose  of 
ventilation,  that  form  of  airway  is  best  that  has  the  shortest 
length  of  perimeter,  for  the  same  area  of  section. 

In  this  respect,  the  circular  airway  is  first;  the  ellipsoidal 
airway  next,  until  the  major  axis  exceeds  2.73  times  the  minor 
axis  when,  for  the  same  area,  the  perimeter  is  equal  to  that 
of  a  square  airway.  The  square  airway  is  then  third  in  the 
series  and  the  rectangular  and  trapezoidal  forms  last. 

There  are,  however,  other  requirements  than  those  of  ven- 
tilation. Haulage  requires  a  level  bottom  for  the  roadway. 
Roof  conditions  or  economy  of  driving  entries  may  put  an 
arched  roof  out  of  the  question,  making  it  necessary  to  adopt 
the  square,  rectangular,  or  trapezoidal  shape.  Again,  a  weak 
coal  and  heavy  side  pressure  may  demand  an  ellipsoidal  shape 
of  section  or  a  special  type  of  timbering  approaching  the 
same.  It  is  not  uncommon  to  arch  the  roof  of  airways  for  a 
distance,  using  either  a  semicircle  or  a  semiellipse  to  form 
the  arch,  the  latter  being  called  a  "flat  arch." 


THEORY  OF  VENTILATION  189 

The  closer  the  ellipse  approaches  the  circle  or  the  nearer  a 
rectangle  comes  to  being  a  square,  the  less  is  the  perimeter 
of  the  airway,  for  the  same  area  of  section.  For  the  same 
length  of  airway,  the  perimeter  is  proportional  to  the  rub- 
bing surface  of  the  airway. 

Similar  Airways. — Two  airways  are  similar  to  each  other 
when  their  cross-sections  are  similar;  the  term  "similar"  has 
no  reference  to  the  length  of  the  airway. 

The  cross-sections  of  -airways  are  similar  when  their  cor- 
responding dimensions  are  proportional,  each  to  each,  and 
their  perimeters  parallel  throughout  or  can  be  so  placed. 

Illustration. — All  circular  or  square  airways  are  similar, 
because  they  have  but  one  dimension,  the  diameter  of  the 
circle  or  the  side  of  the  square,  and  these  dimensions  are, 
therefore,  always  proportional. 

For  example,  one  circular  airway  may  have  a  diameter 
twice  or  three  times  as  great  as  that  of  another  circular  air- 
way; or  the  side  of  a  square  airway  may  be  two  or  three 
times  that  of  another  square  airway;  and  their  perimeters 
can  always  be  placed  so  that  their  circumferences  will  be  con- 
centric or  their  sides  parallel,  each  to  each. 

On  the  other  hand,  the  rectangle,  trapezoid  and  ellipse 
each  have  two  dimensions;  and  while  one  of  these  dimensions 
may  be  two,  three,  etc.,  times  as  great  as  the  corresponding 
dimension  of  another  airway  of  the  same  form,  it  does  not 
follow  that  the  other  dimensions  of  the  two  airways  have  the 
same  proportion;  and  unless  they  do  the  airways  are  not 
similar.  Thus,  a  6  X  8-ft.  airway  and  a  9  X  12-ft.  airway  are 
similar,  because  their  corresponding  sides  have  the  same 
ratio,  or  are  proportional  and  may  be  written 

l  =  &        or6:9::8:12 

A  6  X  8-ft.  airway  and  a  3  X  16-ft.  airway,  however,  are  not 
similar  airways,  though  they  have  equal  sectional  areas 
6  X  8  =  48  sq.  ft.,  and  3  X  16  =  48  sq.  ft.);  because  the 
second  airway  is  twice  as  wide  but  only  half  as  high  as  the 
first. 


190 


MINE  GASES  AND   VENTILATION 


It  is  important  to  observe  that  in  all  similar  airways,  the 
ratio  of  the  sectional  areas  of  the  airways  is  equal  to  the  square 
of  the  ratio  of  the  corresponding  dimensions.  For  example, 
in  Figs.  30  and  31  showing  two  similar  trapezoidal  sections, 
the  top,  bottom  and  sides  of  the  larger  airway  are  each  twice 
those  of  the  smaller,  and  the  area  of  the  larger  section  is,  there- 
fore, 22  =  4  times  that  of  the  smaller. 

Principle  of  Similar  Airways. — Since  corresponding  dimen- 
sions of  similar  airways  have  a  fixed  ratio,  which  is  the  same 


,      Perimeter-  2*5+6+12  '28  ft. 


U--  .........  -  ...........  24-  ......................  ™ 


FIG.  31. 


for  each  dimension  (diameter,  side,  height  or  width)  it  is 
possible  to  compare  similar  airways  with  respect  to  any  of 
these  dimensions. 

Application. — Assume,  for  example,  the  same  pressure  (p) 
is  applied  to  each  of  two  similar  circular  airways,  and  it  is 
required  to  find  how  the  quantity  of  air  will  vary  in  the  two 
airways.  First  write  the  formula  for  the  quantity  (q),  in 
terms  of  the  pressure  (p)  and  the  dimensions,  area  (a),  perim- 
eter (o)  and  length  (I)  of  the  airway,  and  the  coefficient  of 
friction  (k)',  thus, 


T  = 


pa* 


klo 


Now,  if  the  two  airways  have  the  same  length,  and  are  under 
the  same  pressure,  p,  /  and  k  are  all  constant  and 


vares  as  — 


THEORY  OF  VENTILATION,  191 

But,  the  area  of  a  circle  varies  as  the  square  of  its  diam- 
eter (d2)  and  the  perimeter  varies  as  the  diameter  (d)  ;  hence, 

a3       .          d6 
-  vanes  as  -p  or  simply  as  d5 

Hence, 

q2  varies  as  d5 

In  the  same  manner,  it  can  be  shown  in  respect  to  all 
similar  airways  of  any  form,  that  the  square  of  the  quantity 
varies  as  the  fifth  power  of  any  corresponding  dimension  (d), 
whether  diameter,  side,  height,  or  width. 

Rule.  —  In  comparing  similar  airways  of  equal  length,  for 
the  same  unit  pressure,  the  square  of  the  quantity  ratio  is 
equal  to  the  fifth  power  of  the  dimension  ratio;  and,  for  the 
same  power  on  the  air,  the  cube  of  the  quantity  ratio  is  equal 
to  the  fifth  power  of  the  dimension  ratio. 

Example.  —  If  100,000  cu.  ft.  of  air  is  passing  per  minute,  in  a  6  X  9-f  t. 
airway  under  a  given  pressure,  what  quantity  of  air  will  the  same  pres- 
sure circulate  in  an  airway  8  X  12  ft.  of  the  same  length?  What  quan- 
tity will  the  same  power  circulate? 

Solution.  —  These  airways  are  similar  because  their  corresponding 
dimensions  are  proportional  6  :  8  :  :  9  :  12.  Therefore,  calling  the  required 
quantity  x, 


8V-/4V 
~\3/ 


1024 
243 


4.214  =  2.0528 


100,000 

x  =  100,000  X  2.0528  =  205,280  cu.  ft.  per  min. 
Assuming  a  constant  power  on  the  air: 


x  =  100,000  X  1.6152  =  161,520  cu.  ft.  per  min. 

Resistance  of  Airways.  —  ^The  resistance  that  an  airway 
offers  to  the  passage  of  air  is  of  two  kinds:  frictional  resist- 
ance due  to  the  rubbing  of  the  air  on  the  inner  surface  of 
the  airway,  and  the  resistance  due  to  the  air  striking  against 
obstructions  such  as  timbers,  roof  falls,  sharp  bends,  etc. 

How  Resistance  Varies.  —  In  mine  ventilation,  the  entire  re- 
sistance of  airways  is  estimated  on  a  frictional  basis,  accord- 


192  MINE  GASES  AND  VENTILATION 

ing  to  the  extent  of  rubbing  surface  and  the  velocity  of 
the  air.  It  is  assumed  that  when  the  velocity  of  the  air 
current  is  doubled,  each  resisting  particle  in  the  airway  is 
struck  twice  as  often  and  twice  as  hard,  by  the  passing  air, 
which  makes  the  resistance  offered  by  each  particle  2X2  =  4 
times  as  great  as  before.  If  the  velocity  is  increased  three 
times,  the  resistance  of  each  particle  is  increased  3X3  =  9 
times,  etc.  On  this  assumption,  the  resistance  of  an  airway 
varies  as  the  extent  of  rubbing  surface  (s)  and  the  square 
of  the  velocity  (v  X  v  =  v2),  or  as  the  expression  sv*  for 
that  airway. 

Unit  Resistance  or  Coefficient  of  Friction. — The  amount  of 
resistance,  per  unit  of  rubbing  surface  (1  sq.  ft.),  for  a  unit 
velocity  (1  ft.  per  min.)  is  called  the  unit  of  resistance  or 
the  coefficient  of  friction.  The  values  most  commonly 
adopted  for  this  unit  are 

k  =  0.00000002  lb.  (Atkinson,  revised) 
k  =  0.00000001  lb.  (Fairley) 

Calculation  of  Resistance  of  Airways. — To  find  the  resist- 
ance of  an  airway  for  any  given  velocity,  multiply  the  unit 
resistance  (k)  by  the  rubbing  surface  in  square  feet  (s),  and 
that  product  by  the  square  of  the  velocity  in  feet  per  minute 
(y2);  the  final  product  will  be  the  total  resistance  (R),  in 
pounds,  as  expressed  by  the  formula 

R  =  ksv2 

Example. — Find  the  resistance  of  an  airway  having  60,000  sq.  ft. 
of  rubbing  surface,  when  the  velocity  of  the  air  current  is  800  ft.  per 
min. 

Solution. — The  resistance,  in  this  case,  is 

R  =  0.00000002  X  60,000  X  8002  =  768  lb. 
SYMBOLS  AND  FORMULAS 

Most  of  the  rules  of  mine  ventilation  are  expressed  by 
means  of  formulas,  which  show  at  a  glance  the  relation  of 
the  several  factors  to  each  other,  and  make  possible  many 
transformations  and  developments. 

Symbols. — As  far  as  practicable,  the  same  symbols  are  used 
throughout  to  designate  the  same  factors;  and  these  are,  for 


THEORY  OF  VENTILATION  193 

the  most  part,  those  symbols  commonly  employed  in  ventila- 
tion, as  being  the  initial  letter  of  the  word  for  which  they 

stand.  For  example,  p  =  pressure;  v  =  velocity;  #  =  quan- 
tity, etc.  The  following  table  gives  the  more  important  sym- 
bols used : 

TABLE  OF  COMMON  SYMBOLS,  MINE  VENTILATION 

A  =  area  of  regulator,  sq.  ft. 

a  =  area  of  airway,  sq.  ft. 

B  =  height  of  barometer,  in. 

C  =  Centigrade  reading,  deg. 

c  —  constanl, 

D  =  depth  of  shaft,  ft. 

d  =  diam.  or  side  of  airway,  ft. 

F  =  Fahrenheit  reading,  deg. 

g  =  gravity,  ft.  per  sec. 

H  =  horsepower,  33,000  ft.-lb.  per  min. 

h  =  height  of  air  column,  ft. 

K  =  Efficiency  of  fan,  per  cent. 

k  =  coefficient  of  friction,  0.00000002 

I  =  length  of  airway,  ft. 

n  =  number  of  revolutions,  r.p.m. 

o  —  perimeter  of  airway,  ft. 

P  =  total  pressure,  lb. 

p  —  unit  pressure,  lb.  per  sq.  ft. 

Q  =  total  circulation  of  air,  cu.  ft.  per  min. 

q  =  single  current,  cu.  ft.  per  min. 

R  =  resistance  of  mine  or  airway,  lb. 

r  =  any  ratio, 

s  =  rubbing  surface  of  airway,  sq.  ft. 

T  =  absolute  or  higher  temperature,  deg. 

t  =  actual  or  lower  temperature,  deg. 

U  =  total  power  on  air,  ,    ft.-lb.  per  min. 

u  =  power,  single  current,  ft.-lb.  per  min. 

v  =  velocity  of  air,  ft.  per  sec. ,  or  ft.  per  min. 

V  =  volume  of  air  or  gas,  cu.  ft. 

W  =  total  weight  of  body,  lb. 

w  =  unit  weight,  lb.  per  cu.  ft. 
X  =  potential  of  mine  or  airway, 
Xp  =  pressure  potential, 
Xu  =  power  potential 

x  —  the  unknown  quantity  whose  value  is  sought 

w.g.  —  water  gage  reading,  in. 
Sp.  gr.  =  specific  gravity, 

13 


1 94  MINE  GASES  A  ND  YEN  TIL  A  TION 

Small  subscript  letters  and  figures  are  frequently  written 
immediately  after  any  symbol  to  show  its  reference  to  a 
particular  kind  or  thing.  For  example,  qi,  q%,  q3,  etc.,  indi- 
cate the  quantities  of  air  passing  in  three  or  more  airways; 
<?«>  %  Qc,  etc.,  indicate  the  quantities  passing  in  Splits  A, 
B,  C,  etc.  In  like  manner,  the  potential  values  of  different 
airways  and  splits  are  indicated  by  Xi,  Xz,  X 3,  etc.;  or  Xa,  Xb, 
Xc,  etc.,  as  the  case  may  be. 

In  some  cases,  two  or  more  subscript  letters  or  figures  are 
used  after  a  single  symbol  to  indicate  its  reference;  as  for 
example,  the  pressure  potential  for  Split  A  is  written  Xpa 
or  the  power  potential  Xua-  The  general  potential,  in  a  split 
circulation,  is  written  XQ;  or  Xp0  and  XUQ  to  indicate  the 
general  pressure  and  power  potentials,  respectively. 

It  is  often  necessary  to  indicate  the  summation  of  a  num- 
ber of  items  of  the  same  kind,  for  which  purpose  the  charac- 
ter £  is  written  before  the  symbol  indicating  the  kind.  For 
example,  ^Xabc  indicates  the  sum  of  the  potential  values  for 
the  splits  A,  B  and  C,  instead  of  writing  Xa  +  Xb  +  Xc. 

In  a  complex  circulation,  consisting  of  a  main  airway  and 
two  or  more  splits,  it  is  often  necessary  to  indicate  the  gen- 
eral split  potentials  by  X0,  Xao,  Xbo,  etc.,  and  the  mine  potential 
by  X.  (See  Fig.  33,  p.  236.) 

Use  of  Formulas. — A  comparatively  few  formulas  form 
the  basis  from  which  practically  all  the  other  formulas  of 
mine  ventilation  are  derived.  These  few  basal  formulas 
also  show  the  true  relation,  one  to  the  other,  of  the  principal 
factors  of  ventilation,  such  as  pressure,  velocity,  quantity, 
power,  rubbing  surface  and  the  sectional  area  of  mine  airways. 

The  understanding  of  these  formulas  makes  it  unnecessary 
to  learn  and  remember  a  large  number  of  rules  of  ventilation. 
A  formula  is  written  as  an  algebraic  equation  in  which  each 
factor  is  expressed  by  its  proper  symbol.  The  equation  shows 
the  equality  of  certain  factors  grouped  in  the  form  of  an 
expression.  For  example,  the  formula 

pa=  ksv2 
shows  the  equality  of  the  total  ventilating  pressure  pa  and 


THEORY  OF  VENTILATION  195 

the  resistance   of  the  airway  when  the  rubbing  surface  is  s 
and  the  velocity  of  the  air  current  v. 

How  Factors  Vary. — It  is  evident,  from  the  inspection  of 
a  formula,  that : 

1.  Any  factor  in  one  member  of  the  equation  varies  directly 
as  any  like  factor  in  the  other  member,  provided  the  other 
factors  remain  constant  and  none  of  the  quantities  expressed 
in  the  formula  are  connected  by  the  signs  plus  (+)  or  minus 

(-)- 

2.  Any   factor  in  either  member  varies  inversely  as  any 
like  factor  in  the  same  member,  with  the  provisions  just  stated 
(1)  above. 

For  example,  the  formula  previously  given    shows  that : 

The  total  ventilating  pressure  (pa)  for  airways  varies  as 
the  resistance  (ksv2)  of  the  airway. 

For  any  given  airway,  a,  s  and  k  being  constant,  the  unit 
pressure  (p)  varies  directly  as  the  square  of  the  velocity  (v2) 
of  the  air  current. 

For  the  same  total  pressure  (pa) ,  in  an  airway,  k  being 
constant,  the  square  of  the  velocity  (v2)  varies  inversely  as 
the  rubbing  surface  (s).  Or,  in  other  words,  the  velocity  (v) 
of  the  air  current  varies  inversely  as  the  square  root  of  the 
rubbing  surface  (\/s  ) . 

For  the  same  velocity  (v)  of  air  and  the  same  rubbing  sur- 
face (s)  in  an  airway,  k  being  constant,  the  unit  pressure  (p) 
always  varies  inversely  as  the  sectional  area  (a)  of  the  airway. 

3.  Again,   transposing  the  formula  for  total  pressure,  the 
formula  for  unit  pressure  producing  a  given  velocity  in  a 
given  airway  or  mine  is 

_  ksv2 

An  inspection  of  this  formula  shows  that: 

The  other  factors  remaining  constant  and  none  of  the 
quantities  being  connected  by  the  signs  plus  (+)  or  minus 
(  — ),  any  factor  in  the  denominator  of  a  fractional  term  form- 
ing either  member  of  the  equation  varies  directly  as  any 
factor  in  the  numerator  of  that  fraction;  and  likewise  as  any 
similarly  placed  factor  in  the  other  member. 


196  MINE  GASES  AND  VENTILATION 

Basal  Formulas. — There  are,  in  fact,  but  two  truly  basal 
formulas,  in  mine  ventilation;  the  one  expressing  the  resist- 
ance that  an  airway  offers  to  the  passage  of  an  air  current 
having  a  certain  velocity;  the  o'her  expressing  the  power  on 
the  air  producing  a  certain  velocity  in  an  airway,  against  a 
certain  resistance.  These  formulas  are  as  follows: 

Resistance  of  airway,     R  =  pa  =  ksv2 
Power  on  the  air,  u  =  pav  =  ksv3 

From  these  two  simple  formulas  as  a  basis,  with  the  aid 
of  a  few  other  recognized  formulas  and  principles  for  deter- 
mining the  quantity,  horsepower,  water  gage,  rubbing  sur- 
face, etc.,  all  ventilation  formulas  are  derived. 

MINE  POTENTIAL  METHODS 

An  Important  Principle. — One  of  the  most  important  prin- 
ciples of  mine  ventilation  may  be  stated  briefly  as  follows: 

Every  airway  or  mine  possesses  a  certain  definite  resisting 
power,  which  is  determined  by  the  ratio  of  its  area  of  passage 
to  rubbing  surface.  For  this  reason,  a  given  power  will  pro- 
duce a  certain  velocity  and  develop  a  certain  resistance,  in  a 
given  airway;  the  velocity  of  the  air  current  varying  in- 
versely as  the  resistance.  Ventilating  pressure  is  caused  by 
and  equal  to  the  resistance  developed.  Power,  then,  creates 
velocity,  which  in  the  airway  develops  resistance;  and  the 
resistance  produces  pressure. 

The  conclusion  is,  therefore,  evident  that  it  is  the  resisting 
power  of  a  mine  or  airway  that  determines  the  velocity  and 
pressure  a  given  power  will  produce  in  that  airway.  The 
airway,  it  is  clear  only  possesses  this  resisting  power  po- 
tentially, its  development  requiring  the  passage,  of  an  air 
current.  Hence, .  it  is  proper  to  term  such  resisting  power, 
expressed  in  terms  of  the  airway,  the  "potential  of  the  airway" 
or  the  "mine  potential,"  in  respect  to  a  mine. 

As  has  been  explained,  the  equivalent  of  the  mine  potential, 
expressed  in  terms  of  the  power,  quantity  or  pressure,  is 
properly  called  the  "potential  of  the  circulation." 


THEORY  OF  VENTILATION  197 

Illustration  of  Formulas. — To  illustrate  the  use  of  formulas 
in  mine  ventilation,  and  to  make  clear  their  application,  the 
following  table  is  given,  in  which  most  of  the  formulas  in 
common  use  are  classified  under  their  proper  heads.  Many 
of  these  formulas,  as  will  be  observed,  are  simple  transposi- 
tions of  another  formula  or  obtained  by  substitution.  The 
calculations,  in  the  table,  all  refer  to  an  airway  5  X  10  ft.  in 
cross-section  and  4000  ft.  long,  passing  an  air  current  of,  say 
25,000  cu.  ft.  per  min.  against  a  pressure  of  12  Ib.  per  sq.  ft. 

The  Airway.— 

Perimeter,  o  =  2(5  +  10)  =  30  ft. 

Length,  I   =  4000  ft. 

Rubbing  surface,  (*  =  lo)       s  =  4000  X  30  =  120,000  sq.  ft. 
'Sectional  area,  o  =  5  X  10  —  50  sq.  ft. 

Power  potential  of  airway  or  mine, 

a  50 

Xu  =:  \/ks     Xu  =~~  ~  =  373'45 


The  Air  Current.— 

q  25,000       _„„  ,, 

Velocity,          v  =  -  v  =  — ^—  =  500  ft.  per  mm. 


a 


-     fe?      .,  _  .  /  12  X  50 

).00000002  X  120,000 

=  500  ft.  per  min. 

300,000 


).00000002  X  120,000 

=  500  ft.  per  min. 
300,000        K/m  ft 

V    =    10    xx    RA    =    500/^  PCr   mm' 


Power  potential  of  the  circulation, 


q  25,000 

u=  ^=  = 


The  square  of  the  pressure  potential  can  always  be  used 
instead  of  the  cube  of  the  power  potential  since  these  are 
equal,  as  expressed  by  the  formula 


198  MINE  GASES  AND  VENTILATION 

Thus,  Xp  =  Xu  \/X~u  =  373.45  \/373.45  =  7217,  nearly 
Pressure  potential, 

Xn  = 


q  25,000 

Xp=Vp      Xp=  =  7217' nearly 


Quantity,  q  =  av  q  =  50  X  500  =  25,000  cu.  ft.  per  mm- 


12  X  50 


).00000002  X  120,000 

=  25,000  cu.  ft.  per  win. 

300,000" 
).00000002  X  120,000 

=  25,000  cu.  ft.  per  min. 

u  300,000 

q  =  -  q  =  — ~y     =  25,000  cu,  ft.  per  mm. 

q  =  Xu\/u     q  =  373.45  \/300,000 

=  25,000  cu.ft.  per  min. 

q  =  Xp\/p     q  =  7217A/12  =25,000  cu.ft.  per  min 

ksv2  0.00000002  X  120,000  X  5002 

Pressure,  p  =  —      p  =  5Q 

=  12  lb.  per  sq.  ft. 
_  ksq2          _  0.00000002  X  120,000  X  25,0002 

p  ~:  T3~     p  =  503 

=  12  lb.  per  sq.  ft. 
u  300,000 


p  =  5.2  w.g.    p  =  5.2  X  2.307  =  12  lb.  per  sq.ft. 
Resistance,  R  =  pa  R  =  12  X  50  =  600  lb. 

R  =  ksv2         R  =  0.00000002  X  120,000  X  5002 

=  600  lb. 

» 

500 


THEORY  OF  VENTILATION  199 

p  12 

Water  gage,  w.g.  =  ^     w.g.  =  ^  =  2.307  +  in. 

Power  on  air,  u  =  kw*       u  =  0.00000002  X  120,000  X  500* 

=  300,000  ft.-lb.  permin. 

ksq*  0.00000002  X  120,000  X  25,000* 

u  =  —  f-        u  =  -  —  r^  -- 

a3  503 

=  300,000  ft.-lb.  permin. 

u  =  qp          u=  25,000  X  12 

=  300,000  ft.-lb.  permin. 


permin. 

u  =  pav        u  =  12  X  50  X  500 

=  300,000  ft.-lb.  permin. 

u  300,000 

Horsepower,    H  =  u  =  --  9.09  hp. 


MEASUREMENT  OF  AIR  CURRENTS 

The  measurement  of  air  currents,  in  mining  practice,  in- 
volves the  careful  observation  of  the  velocity  and  pressure 
of  the  current  and  the  accurate  measurement  of  the  sectional 
area  of  the  airway.  From  these  data  the  volume  and  power 
of  the  air  current  are  determined. 

Requirements.  —  The  mining  laws  of  the  state,  in  most 
cases,  require  a  specified  volume  of  air  per  man,  per  minute, 
circulated  throughout  the  mine.  In  order  to  meet  this  re- 
quirement, it  is  necessary  to  estimate  the  power  that  will 
produce  such  quantity  in  a  given  mine. 

The  Mine  Potential.  —  Every  airway  and  every  mine  has  a 
certain  resisting  power,  in  respect  to  the  circulation  of  air. 
For  this  reason,  the  same  power  will  circulate  different  quan- 
tities of  air  through  airways  that  differ  in  respect  to  either 
their  size  or  length. 

The  formulas  of  mine  ventilation  show  the  following  rela- 
tion of  the  quantity  of  air  circulated  to  the  power  producing 


200  MINE  GASES  AND  VENTILATION 

the  circulation,  and  the  sectional  area  to  the  rubbing  surface 
of  the  airway. 

Quantity  sectional  area 

3/75-=     '-  varies  as     3/     . .  .  ~      =j= 
V  Power  v rubbing  surface 

Or,  say:  quantity  (cu.  ft.  per  min.)  =  q;  power  (ft.  Ib.  per 
min.)  =  u]  sectional  area  (sq.  ft.)  =  a;  and  rubbing  surface 
(sq.  ft.)  =  s;  the  unit  resistance  being  k,  we  have 


\/u       \/ks 

The  first  of  these  expressions,  being  given  in  terms  of  the 
power  and  quantity  of  air  circulated,  may  be  called,  prop- 
erly, the  " potential  of  the  circulation;"  while  the  second  ex- 
pression, being  given  in  terms  of  the  airway,  is  the  "  potential 
of  the  airway,"  or  the  "mine  potential."  The  significance  of 
the  term  "potential,"  in  this  connection,  is  apparent  since  it 
describes  the  capacity  of  an  airway  or  mine  in  respect  to  the 
volume  of  air  it  will  pass,  per  unit  of  power. 

Values  of  the  Potential. — Calling  the  potential  factor  X,  its 
value  for  any  given  mine  or  airway  is  calculated  by  the 
formula 

X  = 


The  value  of  the  potential  for  the  circulation  of  any  quan- 
tity (q),  by  any  power  (u)  or  pressure  (p),  is  found  by  the  formula 


A     -       ~3/= 

\/u 

The  value  of  the  potential  lies  in  the  fact  that  it  gives 
to  every  mine,  or  air  split,  a  definite  value  that  enables  a 
correct  comparison  to  be  made  between  them,  and  the 
proper  type  of  ventilator  and  system  of  ventilation  to  be 
chosen. 

Potential  of  Airway. — Calculate  the  potential  of  an  airway 
6  X  10  ft.,  in  cross-section,  and  2000  ft.  long. 


THEORY  OF  VENTILATION  201 

Solution — The  sectional  area  of  this  airway  is  6  X  10  =  * 
60  sq.  ft.;  the  rubbing  surface  is  2(6  +  10)2000  =  64,000  sq. 
ft.     The  potential  of  the  airway  is,  therefore, 

v          a          60 

X  =     ,  ...__  =    ,.  =  ooz.o 

\/ks      -\/  0.00000002  X  64,000 

Potential  of  Circulation. — What  is  the  value  of  the  poten- 
tial factor  in  the  circulation  of  60,000  cu.  ft.  of  air,  by  10  hp.? 
Solution. — The  potential  of  this  circulation  is 

a  60,000 

X  =  17=  =  -I/TTf^        ^^  =  868'2 

•\u       v  10  X  33,000 

Find  the  potential  value  for  the  same  volume  of  air  when 
circulated  under  a  pressure  of  8  Ib.  per  sq.  ft. 
Solution. — The  potential  value,  in  this  case,  is 


Y        .,*         3/60,0002 
X"-^p--\^-     =  766'3 

Power,  Pressure,  Quantity. — By  transposing  the  formulas 
for  potential,  it  is  possible  to  calculate  the  power  or  pres- 
sure required  to  circulate  any  given  quantity  of  air  against 
any  given  mine  potential;  or  to  find  the  air  volume  a  given 
power  or  pressure  will  produce,  for  any  given  mine  potential. 

Example. — Find  the  (1)  power,  and  (2)  pressure  required  to  circulate 
24,000  cu.  ft.  of  air  through  an  airway  5  X  14  ft.  in  section  and  3000 
ft.  long? 

Solution. — The  area  and  rubbing  surface  of  the  airway  are:  a  = 
5  X  14  =  70  sq.  ft.;  and  *  =  2(5  +  14)3000  =  114,000  sq.  ft.  The 
potential  factor  of  this  airway  is  then 

a_ 70 _ 

~  ^ks  ~  -^0.00000002  X  114,000  ~ 

(1)  Power,          u  =  (-??)     =  (  K'    0  }     =  91,900  ft.-lb.  per  min. 

\A/          \5dl.8  / 

(2)  Pressure,       p  =  J^  =   r'          =  3.83  Ib.  per  sq.  ft. 

p=JL  =  9^900  =383J6  per 
q        24,UUU 

Example. — Find  the  volume  of  air  circulated  in  the  same  mine,  by 
(1)  10  hp.;  (2)  a  pressure  of  7.8  Ib.  per  sq.  ft. 


202 


MINE  GASES  AND  VENTILATION 


Solution. — 

(1)  By  10  hp., 

q  =  X  v^T    =  531.8  <y  10  X  33,000  =  36,750  cu.  ft.  per  min. 

(2)  By  7.8  lb.,  

q  =  X  VlXp  =  531.8  V  531.8  X  7.8  =  34,250  cu.  ft.  per  min. 

Potential  Values  of  Different  Airways. — In  order  to  show 
the  resisting  power  of  airways  of  different  lengths,  for  those 
sizes  in  more  common  use,  the  following  table  has  been  pre- 
pared, showing  the  potential  value  of  each  airway,  as  calcu- 
lated by  the  formula 

Potential  of  airway,  X  = 


Following  this  is  another  table  giving  the  potential  values 
of  different  circulations,  by  which  is  meant  the  circulation  of 
different  volumes  of  air  under  different  pressures  or  water 
gages.  A  comparison  of  the  potential  values  in  these  two 
tables  will  serve  to  show  what  circulation  can  be  obtained  in 
airways  of  given  size  and  length  when  properly  arranged  and 
unobstructed. 

TABLE. — POTENTIAL  VALUES  FOR  DIFFERENT  AIRWAYS 


Length  of  Airway,  Including  Return  (ft.) 


Size  of  airway, 
feet 

1,000             2,000             3,000 

5,000 

8,000       |       10,000 

Potential  value  of  airway 

4  X  10 

485  .  3 

385.0 

336.5 

283.8 

242.6 

225.2 

4  X  12 

557.0 

441.9 

386.2 

325.7 

278.5 

258.5 

4  X  14 

624.8 

495.7 

433.2 

365.4 

312.4 

290.0 

5X8 

497.4 

394.6 

344.9 

290.9 

248.7 

230.9 

5  X  10 

592.8 

470.3 

411.0 

346.7 

296.4 

275.2 

6X8 

582.3 

462.0 

403.8 

340.6 

291.2 

270.3 

6  X  10 

696.2 

552.4 

482.7 

407.2 

348.1 

323.2 

7X8 

664.0 

526.7 

460.4 

388.3 

332.0 

308.2 

7  X  10 

796.0 

631.5 

552.0 

465.5 

398.0 

369.5 

8  X  10 

892.6 

708.1 

618.9 

522.0 

446.3 

414.3 

Potential  Values  of  Different  Circulations. — The  circulation 
of  a  given  quantity  of  air  in  a  certain  airway  or  mine  requires 


THEORY  OF  VENTILATION 


203 


a  certain  pressure  or  water  gage,  which  determines  the  "  poten- 
tial of  the  circulation." 

In  the  following  table,  the  potential  of  the  circulation  is 
calculated  by  the  formula 


3    Q2  3   I         Q2 

ion,     X  =  \  —  =  Al-  0 

\  p        \5.2w.g. 


Potential  of  circulation, 

TABLE.  —  POTENTIAL  VALUES  FOR  DIFFERENT  CIRCULATIONS 


Water 
Siage 
(in.) 

Pressure 
(lb.  per 
sq.  ft.) 

Volume  of  air  circulated  (cu.  ft.  per  min.) 

10,000 

15,000     |      25,000 

50,000 

75,000 

100,000 

Potential  value  of  circulation 

0 

31.2 

147.4 

193  .  2 

271.6 

431.1 

564.9 

684.4 

5 

26.0 

156.7 

205.3 

288.6 

458.1 

600.3 

727.2 

4 

20.8 

168.8 

221.2 

310.9 

493.5 

646.7 

783.4 

3 

15.6 

185.8 

243.4 

342.2 

543.2 

711.8 

862.2 

2K 

13.0 

197.4 

258.7 

363.6 

577.2 

756.3 

916.3 

2 

10.4 

212.6 

278.6 

391.7 

621.8 

814.8 

987.0 

1M 

7.8 

234.0 

306.7 

431.1 

684.3 

896.8 

1,086.4 

1 

5.2 

267.9 

351.1 

493.5 

783.4 

1,026.5 

1,243.6 

X 

2.6 

337.6 

442.3 

621.8 

987.0 

1,293.4 

1,566.8 

Comparing  this  table  with  that  on  the  preceding  page 
shows  that  to  pass  a  current  of  25,000  cu.  ft.  per  min.  through 
an  airway  of  5  X  8  ft.,  3000  ft.  long,  including  the  return  will 
require,  practically,  a  3-in.  water  gage.  This  is  ascertained 
by  observing  that  the  potential  value  of  an  airway  5  X  8  ft., 
3000  ft.  long,  as  given  in  the  first  table,  is,  say  345.  Then 
find  the  water  gage  corresponding  as  nearly  as  possible  to 
this  value,  in  the  second  table,  in  the  vertical  column  for 
25,000  cu.  ft.  per  min.  The  potential  of  the  circulation  of  this 
air  volume  under  a  3-in.  gage  is,  say  342,  showing  that  a 
3-in.  gage  is  a  little  in  excess  of  what  is  required  to  circulate 
25,000  cu.  ft.  of  air  per  minute  in  a  5  X  8-ft.  airway,  3000  ft. 
long,  including  the  return. 

Effect  of  Splitting  on  Mine  Potential. — As  a  mine  is  devel- 
oped and  its  airways  extended,  it  becomes  impracticable  to 
carry  the  air  in  a  single  current  throughout  the  entire  length 
of  the  airways,  as  the  water  gage  then  increases  directly  as 


204  MINE  GASES  AND  VENTILATION 

the  length  or  distance  of  air  travel.  To  avoid  this  difficulty, 
the  air  must  be  divided  or  " split"  one  or  more  times;  so  that 
there  will  be  two  or  more  separate  currents  in  the  mine. 
Each  of  these  currents  is  called  a  " split  of  air,"  or  simply 
a  "split"  (see  p.  219). 

It  should  be  observed  that  dividing  the  current  does  not 
change  the  total  rubbing  surface  (s)  in  the  mine;  but  the 
area  of  passage  is  increased  in  proportion  to  the  number  of 
splits  or  currents.  Calling  the  number  of  equal  splits  n,  the 
area  of  passage  (p.  211),  in  splitting  an  air  current  is  na, 
and  the  formula  for  the  potential  can  be  written: 

Split  potential,  X  =  ~TT= 

V  ks 

Since  the  rubbing  surface  (s),  the  sectional  area  (a)  and 
the  coefficient  (k)  are  constant,  the  potential  (X )  varies  as  n, 
or  as  the  number  of  equal  splits  or  currents.  Therefore,  any 
of  the  airway  potentials  of  the  first  table  can  be  multiplied  2, 
3,  4,  etc.  tunes  according  to  the  number  of  splits  or  currents 
employed. 

For  illustration,  suppose  the  airways  of  a  mine  are  5  X  10 
ft.  and  have  a  total  length,  including  return,  say  10,000  ft.; 
and  the  required  circulation  is  100,000  cu.  ft.  per  min.  The 
velocity  of  the  ah-  should  not  exceed,  say  500  ft.  per  min., 
in  the  airways.  This  will  require  a  total  area  of  passage"  of 
100,000  -^  500=  200  sq.  ft.  But  the  sectional  area  of  these 
airways  is  5  X  10  =  50  sq.  ft.;  and  there  must,  therefore,  be 
200  -s-  50  =  4  splits  or  currents  to  comply  with  the  conditions 
named.  The  potential  value,  as  given  in  the  table,  for  a  single 
current,  is,  say  275;  and  the  mine  potential  for  four  splits  is, 
therefore,  4  X  275  =  1100.  By  referring,  now,  to  the  second 
table  giving  the  values  of  the  potential  of  circulation,  it  is 
found  that  a  potential  value  of  1100,  in  the  circulation  of 
100,000  cu.  ft.  per  min.  shows  a  water  gage  between  1  and  1J^ 
in.  The  true  value  may  be  found  by  interpolation,  if  desired, 
and  is  1.46  in. 

The  potential  value  of  any  desired  circulation  of  air,  as 
compared  with  the  potential  value  or  "potential  factor"  of  the 


THEORY  OF  VENTILATION  205 

proposed  mine  or  airway  is  thus  seen  to  have  an  important 
practical  value  that  commends  it  to  all  students  of  mining. 

Example. — It  is  proposed  to  open  a  mine  in  a  6-ft.  seam  of  coal  and 
provide  for  a  capacity  of  1000  tons  a  day*  A  general  estimate  is  de- 
sired of  the  requirements  for  the  proper  ventilation  of  the  mine,  under 
working  conditions.  In  other  words,  what  volume  of  air  will  be  re- 
quired and  what  will  be  the  approximate  water  gage  and  horsepower 
necessary  for  the  circulation  of  such  quantity  in  this  mine  ? 

Solution. — Assuming  an  average  daily  output  of  2.5  tons  of  coal  per 
miner,  the  number  of  miners  working  will  be  1000  -J-  2.5  =  400.  Then 
allowing  for,  say  150  loaders  and  50  company  men  including  bosses,  the 
total  number  of  men  in  the  mine  will  be  600,  for  whom  the  quantity  of 
air  specified  by  law  must  be  provided. 

Assume  that  the  mine  generates  considerable  gas  and  to  cover   all 
requirements,  estimate  on  supplying  200  cu.  ft.  of    air   per  man,  per 
minute,  which  gives  a  total  required  air  volume  of  200  X  600   =  120,000 
cu  ft.  per  min. 

In  order  to  estimate  approximately  what  water  gage  will  result  in  the 
circulation  of  this  quantity  of  air,  it  is  necessary  to  decide  on  the  size  of 
the  entries;  and  make  the  sectional  area  such  as  will  allow  of  a  safe  maxi- 
mum velocity  of  the  air  current  in  the  cross-headings  and  find  the  number 
of  splits  required  to  meet  these  conditions. 

In  this  case,  suppose  all  entries  to  be  6  X  10  ft.,  giving  a  sectional 
area  of  60  sq.  ft.;  and  the  mine  being  gassy,  say  the  velocity  of  the  air 
current  on  all  cross-headings  or  splits  must  not  exceed  360  ft.  per  min. 
This  condition  will  require  a  total  area  of  passage  or  the  sum  of  the 
sectional  areas  of  all  the  splits,  120,000  -;-  360  =  333  sq.  ft.  But  the 
area  of  the  entries  being  each  60  sq.  ft.,  the  number  of  splits  required  to 
give  this  area  of  passage  and  thus  keep  the  velocity  of  the  air  currents 
in  the  splits  within  the  specified  limit  is  333  -f-  60  =  5.5,  say  6  splits  or 
pairs  of  cross-headings. 

The  next  step  is  to  decide  on  the  distance  each  pair  of  cross-headings 
will  be  driven,  from  which  the  extent  of  rubbing  surface  can  be  approxi- 
mately estimated.  For  example,  assume  the  cross-headings  to  be  driven, 
say  2000  ft.  on  each  side  of  the  main  heading,  making  4000  ft.  of  entry, 
including  the  return,  in  each  split.  The  total  length  of  entry  for  the  six 
splits  is  then  6  X  4000  =  24,000  ft.  Assume  the  main  headings  are 
driven  four  abreast,  so  as  to  provide  two  intake  haulage  roads  affording 
separate  tracks  for  the  empty  and  loaded  trips;  and  two  return  airways. 

If  the  cross-entries  are  turned  to  the  right  and  left  of  the  main 
headings,  every  500  ft.,  the  length  of  these  headings  may  be  taken  as 
3  X  500  =  1500  ft.,  giving  a  total  length  for  the  four  headings  4  X 
1500  =  say  6000  ft.  The  total  length  of  all  entries  in  the  mine  may 
thus  be  assumed  as  24,000  +  6000  =  30,000  ft. 


206  MINE  CASES  AND  VENTILATION 

The   estimated   rubbing  surface   is  then   s  =  2(6  +  10)  X  30,000  = 
900,000  sq.  ft.;  and  the  mine  potential  is 

6a  _6X60 

-A    —       ,,  —  -   —      \  .  —    —    1  044 

\/ks      ^0.00000002  X  960,000 

This  is  only  an  approximately  correct  value  for  this  mine,  because 
the  six  splits  do  not  start  from  the  shaft  bottom. 

The  water  gage  required  is  then  calculated  from  the  mine 
potential  and  the  air  volume;  thus, 

Q2  120,0002 

= 


5.2  X  13443 

It  will  be  safe  to  assume,  from  the  above  calculation,  that 
the  proposed  mine  can  be  properly  ventilated  by  the  circula- 
tion of  120,000  cu.  ft.  of  air  per  minute  under  a  water  gage  of 
say  1.5  in.,  providing  for  six  main  air  splits  as  described,  and 
making  due  allowance  for  possible  conditions. 

The  horsepower  required  to  produce  this  circulation,  assum- 
ing a  general  efficiency  of  K  =  60  per  cent,  is 

„       0(5.2  w.0.)        120,000  (5.2  X  1.5) 


0.60  X  33,000 


=47+,  say  50^. 


Example.  —  Find  the  unit  pressure,  water  gage  and  horsepower  re- 
quired to  circulate  80,000  cu.  ft.  of  air  per  minute  in  a  mine  in  two  equal 
splits.  The  airways  are  all  8  X  10  ft.,  and  have  a  total  length  of  12,000 
ft.,  including  the  return  airways. 

Solution.  —  The  sectional  area  of  the  airways,  in  this  case,  is  a  =  8  X 
10  =  80  sq.  ft.;  the  perimeter  is  o  =  2(8  +  10)  =  36  ft.  The  potential 
of  the  airway  for  two  splits  is  then 

na  2  X  80  =  ?8() 


\/klo       -^0.00000002  X  12,000  X  36 
The  unit  pressure  is 

Q*       80,000* 

P  =  -£,  =:    78Q3      =  say  13.5  Ib.  per  sq.  ft. 

The  corresponding  water  gage  is  13.5  -s-  5.2  =  say  2.6  in. 

The  horsepower  on  the  air,  as  calculated  from  the  above  unit  pressure, 


Qp  80,000X13.5 

B  =  3^000   =  33,000" 


THEORY  OF  VENTILATION  207 

Or,  the  horsepower  may  be  found  directly  from  the  mine  potential, 
as  follows: 


„ 

~ 


33,000 


/#\3  __  i     /8o,ooo\» 

\X]     ~  33,000  V   780    ) 


Example.  —  Find  the  quantity  of  air  in  circulation  in  four  equal  splits 
in  a  mine,  when  the  size  of  the  airways  is  5  X  14  ft.  and  the  total  length 
of  airways  in  all  the  splits,  including  the  returns  in  each  case,  is  40,000 
ft.  ;  the  water  gage  at  the  shaft  bottom  where  the  air  is  divided  being  3  in. 

Solution.  —  The  rubbing  surface,  in  this  case,  is  s  =  40,000  X  2(5  + 
14)  =  1,520,000  sq.  ft.,  and  the  sectional  area  of  each  airway  5  X  14  = 
70  sq.  ft.  The  mine  potential  for  four  splits  is  then 

X  =  —  J^^=  =  897 

\/ks        \/6.  00000002  X  1,520,000 

The  quantity  of  air  in  circulation  under  a  3-in.  water  gage  is  then 


w.flO 
=F  897  \/897  -T-  5.2  X  3  =  say  106,000  cu.  ft.  per  min. 

Caution, — In  the  calculation  of  all  problems  in  mine  ven- 
tilation, regard  must  be  had  to  the  conditions  with  respect 
to  the  power  and  the  pressure  producing  or  resulting  from 
the  circulation  of  the  air  in  the  mine. 

Both  the  power  and  the  pressure  are  commonly  said  to 
produce  the  circulation;  but,  as  a  matter  of  fact,  it  is  the 
power  that  produces  the  circulation,  while  the  pressure  is 
the  result  and  measured  by  the  resistance  of  the  mine  or 
airway. 

Unfortunately,  these  factors  do  not  vary  alike,  but  the 
cube  root  of  the  power  varies  as  the  square  root  of  the  pres- 
sure; or,  more  simply,  the  cube  root  of  the  power  ratio,  in  any 
mine  or  airway,  is  equal  to  the  square  root  of  the  pressure 
ratio,  for  the  same  circulation;  thus, 

El 

p* 

For  example,  in  what  proportion  must  the  power  be  in- 
creased in  order  to  double  the  pressure  (py/pi  =  2)? 

\/ 'power  ratio  =  \/2  =  1.414 
power  ratio  =  1.4143  =  2.828 


208  MINE  GASES  AND  VENTILATION 

In  other  words,  if  10  hp.  on  the  air  produces  a  given  pres- 
sure or  water  gage  in  a  certain  mine  or  airway,  it  will  re- 
quire 2.828  X  10  =  28.28  hp.  to  double  that  pressure  or  gage. 

Use  of  Potential  Factors. — Attention  has  been  drawn  to  the 
potentiality  of  an  airway  or  mine,  in  respect  to  the  resistance 
it  can  offer  to  the  passage  of  air,  by  virtue  of  its  rubbing  sur- 
face (s)  and  its  sectional  area  (a).  The  potential  of  an 
airway  or  mine  is  the  factor  that  determines  the  quantity  of 
air  such  airway  or  mine  will  pass,  for  any  given  power  or 
pressure.  It  is  important,  in  the  use  of  the  potential,  there- 
fore, to  consider  whether  the  pressure  or  power  is  in  question. 

F.or  every  airway  or  mine,  therefore,  there  is  a  power  po- 
tential (Xu)  and  a  pressure  potential  (Xp).  The  cube  of  the 
power  potential  is  equal  to  the  square  of  the  pressure  poten- 
tial, for  the  same  mine  or  airway,  giving  the  equal  values. 

'x  3  -  x  ^  -  t  -  £!  -  **_ 

u       p-      klo 

An  inspection  of  these  equal  values  shows  that : 

1.  The  quantity  of  air  a  given  power  will  circulate  varies 
as  the  power  potential  of  the  airway  or  mine. 

2.  The  quantity  of  air  a  given  pressure  will  circulate  varies 
as  the  pressure  potential  of  the  airway  or  mine. 

Hence,  in  comparing  the  circulations  in  different  airways 
or  mines,  a  constant  power  requires  the  use  of  the  power  po- 
tential, and  a  constant  pressure,  the  pressure  potential. 

Other  Potential  Formulas. — Transposing  the  values  given 
above  makes  it  possible  to  calculate  the  power  or  pressure 
required  to  circulate  a  given  quantity  of  air  in  a  certain  air- 
way or  mine  directly  from  its  potential  factor. 


~   I  Y   )        :    V  2 

\-A  u/          •    -A  p 


It  is,  likewise,  possible  to  calculate  the  quantity  of  air  a 
given  power  or  pressure  will  circulate  against  any  given  po- 
tential factor  representing  a  certain  airway  or  mine,  by 
simply  multiplying  the  cube  root  of  the  power  or  the  square 


THEORY  OF  VENTILATION  209 

root  of  the  pressure  by  the  corresponding  potential  of  the  air- 
way or  mine  as  expressed  by  the  following  formulas : 

q  =  Xu\/u 
q  =  Xp\/p 

A  few  examples  will  serve  to  make  the  use  of  these  for- 
mulas clear  and  to  show  their  practical  application,  in  the 
rapid  estimation  of  what  is  required  in  the  proposed  develop- 
ment of  mines,  in  order  to  make  suitable  provision  for  their 
proper  ventilation. 

EXAMPLES  FOR  PRACTICE 

1.  If  25  hp.  produces  a  water  gage  of  1.5  in.,  in  a  certain  mine,  what 
water  gage  will  40  hp.  produce  in  the  same  mine? 

Solution. — Since  the  square  root  of  the  pressure  or  water-gage  ratio 
is  equal  to  the  cube  root  of  the  power  ratio,  calling  the  required  water 
gage  x, 


=  1.172  =  1.37,  nearly 
l.o 
x  =  1.5  X  1.37  =  2.05  in. 

2.  It  is  proposed  to  provide  for  the  circulation  of  75,000  cu.  ft.  of  air, 
in  two  generally  equal  splits,  the  airways  including  the  return  in  each 
split  being  6  X  10  ft.  in  section  and  about  8000  ft.  long,  (a)  Find  the 
power  potential  for  the  entire  mine ;  and  (6)  calculate  from  that  both  the 
power  and  the  water  gage  of  the  circulation. 

Solution. — (a)  The  sectional  area  of  the  airways,  in  this  case,  is  a  = 
6  X  10  =  60  sq.  ft.;  the  total  rubbing  surface  in  the  mine,  s  =  2  X 
2(6  +  10)8000  =  512,000  sq.  ft.  Substituting  these  values  and  that  for 
the  coefficient  of  resistance  fc  =  0.00000002  in  the  formula  for  power 
potential  of  mine, 

v          na  2  X  60  __OA 

Xu  =     ,, =  •  . ,          =  552.6 

\/ks      y/0.00000002  X  512,000 

The  power  on  the  air  required  to  circulate  75,000  cu.  ft.  of  air  against 
this  potential  is,  then, 

3=  2,500,000  ft.-lb.  permin. 

The  water  gage,   as  calculated  directly  from  the  power  potential, 
v  =  552.6,  is 

q*  75,0002  aA1  . 

W'g'  =  5^X7  =5.2  X  552.63  =  6.41  in. 
Or,  the  water  gage  may  be  found  thus 

w.g.  =  2,500,000  4-  (5.2  X  75,000)  =  6.41  in. 

14 


210  MINE  GASES  AND  VENTILATION 

3.  (a)  Calculate  the  value  of  the  pressure  potential  for  the  entire 
mine  mentioned  in  the  preceding  question,  the  airways  being  6X10  ft. 
in  section  and  about  16,000  ft.  long,  including  the  return,  assuming  as 
before  two  equal  splits;  and  (6)  calculate  from  this  pressure  potential  the 
power  that  will  produce  the  desired  circulation  of  air;  namely  75,000  cu. 
ft.  per  min.  and  the  resulting  water  gage. 

Solution.  —  (a)  The  total  rubbing  surface  is  s  =  2(6  +  10)  16,000  = 
512,000  sq.  ft.  For  two  equal  splits,  the  area  of  passage  in  this  mine  is  a 
=  2(6  X  10)  =  120  sq.  ft.  The  mine  pressure  potential  is  then 


X,  -  «  V£  -  12°  Vo. 


2° 


o.00000002X  512,000 
(b)  The  power  on  the  air,  calculated  from  the  pressure  potential,  is  then, 


u  =  -vT  =  =  say  2,500,000  ft.-lb:  per  min. 


The  water  gage,  calculated  in  the  same  manner,  is 
2  2 


4.  What  volume  of  air  will  10  hp.  circulate  in  an  airway  6X8  ft.,  in 
section,  and  2500  ft.  long? 

.  Solution.  —  The  sectional  area  of  this  airway  is  a  =  6  X  8  =  48  sq.  ft.  ; 
the  rubbing  surface  2(6  -f  8)  2500  =  70,000sq.  ft.  The  power  potential 
is  therefore 

a  =  429.1,  nearly. 


-0.00000002  X  70,000 
For  10  hp.  on  the  air,  the  quantity  of  air  in  circulation  in  this  airway  is 
q  =  Xu\/^  =  429.1-^10  X  33.000  =  say  30,000  cu.  /«,.  per  min. 

5.  (a)  What  quantity  of  air  will  be  circulated,  in  the  airway,  in  the  last- 
example,  under  a  3-in.  water  gage;  and  what  power  on  the  air  will  be 
necessary  to  develop  this  quantity  and  gage?  (6)  What  was  the  original 
water  gage  when  10  hp.  circulated  30,000  cu.  ft.  of  air,  in  this  mine? 

Solution. — (a)  Since  the  square  of  the  pressure  potential  is  equal  to  the 
cube  of  the  power  potential 

Xp  =  V~X*U  =  A/429. 13  =  8890,  nearly 

Then,  q  =  Xp  V7>  =  8890  A/5.2  X  3  =  say  35,000  cu.  ft.  per  min. 
The  power  required  to  produce  a  3-in.  water  gage  is 
35,000  X  3  X  5.2 


THEORY  OF  VENTILATION  211 

(Jo)  The  previous  water  gage  due  to  the  circulation  of  30,000  cu.  ft., 
in  this  mine,  under  10  hp.  can  be  calculated  in  several  ways;  but  most 
simply,  thus, 

=  10  X  33,000  . 

W'9'  ~  5.2  X  30,000 

The  calculation  may  also  be  made  from  the  potential ;  thus, 

g2  30,  OOP2 

W'Q'~  5.2X\  ~  5.2  X429.P 

Area  of  Passage. — It  is  important  to  notice  that  the  poten- 
tial value  for  any  mine  is  determined  by  its  area  of  passage 
with  respect  to  the  resisting  power  of  its  rubbing  surface. 
For  a  single  air  current  the  area  of  passage  is  the  sectional 
area  (a)  of  the  airway.  For  2,  3,  etc.,  equal  splits  the  area 
of  passage  is  2a,  3a,  etc.;  for  n  equal  splits  the  area  of  pas- 
sage, for  the  mine,  is  na. 

The  unit  of  resistance  being  k,  the  resisting  power  of  the 
entire  airway  or  mine  is  indicated  by  ks;  and  the  potential 
values  of  the  mine  with  respect  to  power  and  pressure,  respec- 
tively, are  thus  expressed 

Mine  power  potential,       Xu  — 


Mine  pressure  potential,  Xp  =  \/   j~~  =  n<l  \l 


na 
ks 


It  should  be  observed  that  the  mine  power  potential  varies 
as  the  number  of  equal  splits  or  currents,  which  is  not  true  of 
the  pressure  potential  of  a  mine.  This  fact  has  an  important 
application,  since,  for  the  same  mine,  the  rubbing  surface 
being  constant,  the  number  of  splits  (n)  is  equal  to  the  power- 
potential  ratio.  An  example  will  serve  to  make  this  clear. 

Example. — Suppose  it  is  desired  to  ascertain  quickly  how  many  equal 
splits  would  pass  the  same  quantity  of  air  (75,000  cu.  ft.  per  min.),  under 
a  2-in.  water  gage,  in  Example  3,  previously  given  where  two  splits  of 
air  gave  a  water  gage  of  6.41  in.,  the  power  remaining  constant. 

Solution. — From  the  equat'ons  expressing  the  potential  values  pre- 
viously given  (p.  208),  it  appears,  for  the  same  quantity  of  air  in  circula- 
tion, the  pressure  or  water  gage  varies  inversely  as  the  cube  of  the  power 
potential.  But,  since  the  power  potential  varies  as  the  number  of 
splits  in  a  mine,  it  follows  that,  for  the  same  quantity  of  air  in  circula- 


212  MINE  GASES  AND  VENTILATION 

tion,  the  power  remaining  constant,  the  pressure  or  water  gage  varies 
inversely  as  the  cube  of  the  number  of  splits. 

In  other  words,  for  the  same  quantity  of  air,  and  constant  power, 
the  pressure  or  water-gage  ratio  is  equal  to  the  cube  of  the  inverse 
ratio  of  the  number  of  splits.  In  this  case,  calling  the  required  number 
of  splits  n,  the  split  ratio  is  n/2,  and  the  corresponding  water-gage  ratio 
2/6.41,  and  we  write 

3.205 


2/  2 

n  =  2v/3.205  =  2.95,  say  3  splits. 

The  reference,  thus  far,  has  been  to  equal  division  of  the 
air  current  and  the  rules  and  formulas  given  above  apply 
strictly,  only  to  mines  in  which  the  air  current  is  divided  at  or 
near  the  main  entrance  and  passes  through  the  mine  in  two 
or  more  separate  and  equal  splits. 

Part  Potential  Value.  —  The  part  potential  value  is  found 
by  omitting  k  in  the  calculation,  and  writing  it  outside  the 
parenthesis.  The  relative  potential  obtained  by  canceling 
common  factors  cannot  be  used  here.  The  relative  potential, 
so  much  used  in  the  calculation  of  the  splitting  of  air  cur- 
rents, can  only  be  employed  when  the  potential  appears  as  a 
ratio  (see  p.  221.) 

General  Potential  of  a  Mine.  —  An  important  application  of 
the  potential  method,  in  mine  ventilation,  is  the  calculation 
of  the  potential  value  for  the  entire  mine  when  the  airways 
and  shafts  are  of  various  dimensions. 

Example.  —  Calculate  the  general  mine  power  potential  in  the  following 
mine,  shafts  1250ft.  deep: 

Area       Rub.  Sur. 

Shafts,  upcast  and  downcast,  8  X  10  ft.,  2500  ft.  80  90,000 

Main  airway  ("A"  seam),  6  X  10  ft.,  3750  ft.  60  120,000 

Cross-headings  ("  A"  seam),  6X    8  ft.,  2500  ft.  48  70,000 

Tunnel  to  "B"  seam,  5X8  ft.,    500  ft.  40  13,000 

Return  air  course  ("B"  seam),  5  X  14  ft.,  5500  ft.  70  209,000 

Solution.  —  The  total  power  producing  a  given  circulation,  is  clearly 
equal  to  the  sum  of  the  powers  absorbed  in  the  several  sections  of  the 
mine,  as  expressed  by  the  following  general  formula: 

kO3 


H  = 


I  1  1  1  \ 

\YT3  +  xT3  +  !x73+  etcv 


#33,000 

It  will  be  readily  observed  that  this  general  formula,  for  a  mine  of 


THEORY  OF  VENTILATION  213 

various  sections  (K  being  the  coefficient  of  efficiency  of  the  ventilator), 
is  derived  from  the  power  formula 

Q3         1 


~  #33,000  \ Xj        #33,000  Xu3 

But,  since  l/Xuz  =  k  s/a3  and  k  being  constant,  it  is  much  simpler  in 
using  the  above  general  formula,  to  factor  and  write  k  outside  of  the 
parenthesis,  which  makes  each  of  the  potential  values  within  the  paren- 
thesis what  may  be  called  a  ''part  potential"  whose  value  is,  omitting  k, 

Part  potential  Xu  =  -£=;  and  _1_  =  JL 

Now,  calculating  the  value  of  l/Xu3  =  s/a3,  for  each  separate  section 
of  air  passage  in  the  mine  given  above, 


Shafts, 
Main  airway  ("A"  seam), 
Cross-headings  ("A"  seam), 
Tunnel  to  "B"  seam, 
Return  air  course  ("B"  seam), 

1 

90,000 

01  7^W 

I1 

80  X  80  X  80 
120,000 

.l/Oo 

=  0.5555 
n  ft  '-i  '-in 

1 

60  X  60  X  60 
70,000 

I3 

48  X  48  X  48 
13,000 

=  0.2031 
-  0.6093 

1 

40  X  40  X  40 
209,000 

70  v  7n  s/  7n 

Potential  factor  for  entire  mine  v— - 2.1767 

Ao"1 

The  part  power  potential  for  this  mine  is  therefore 

X0  =  -.  -.— =  0.7716 

V  2. 1767 

Example. — (a)  From  the  part  power  potential  calculated  for  the  mine, 
in  the  preceding  example,  find  the  horsepower  required  to  circulate 
30,000  cu.  ft.  of  air  per  minute  in  a  single  current,  assuming  the  ventilat- 
ing fan  to  have  a  mechanical  efficiency  K  =  60  per  cent.  (/>)  What  water 
gage  will  be  produced  by  the  resistance  in  the  mine,  for  this  circulation? 

Solution. — (a)  The  required  horsepower  of  the  ventilator  is 

kQ3     _1_  _  0.00000002  X  30,000*  1  , 

"  #33,000  *o3  "         0.60  X  33,000        X  0.77163 

(b)  The  mine  water  gage  due  to  this  circulation  is 

kQ*          0.00000002  X  30,0002 
w-°'  =  6AX?    =          5.2X0.77163 

General  Mine  Potential,  Equal  Splits. — It  is  possible  to  calculate  the 
general  mine  potential  when  there  are  two  or  more  airways  of  equal 
dimensions,  by  simply  multiplying  the  common  sectional  area  by  the 
number  of  airways,  as  shown  by  the  following  example: 


214  MINE  GASES  AND  VENTILATION 

Example. — A  drift  mine  is  opened  on  the  triple-entry  system.  It  is 
proposed  to  drive  the  main  intake  7X10  ft.  in  section,  a  distance  of 
3000  ft.  to  the  boundary.  The  cross-entries  are  to  be  driven  double, 
5  X12  ft.  in  section  and  1500  ft.  to  the  side  lines  on  each  side  of  the  main 
road,  making  in  all  6000  ft.  of  cross-entries,  including  the  returns.  The 
main-return  airways,  on  each  side  of  the  main  intake  are  each  7X12  ft. 
in  section  and  3000  ft.  long.  Calculate  (a)  the  horsepower  on  the  air; 
and  (6)  the  water  gage  produced,  for  a  circulation  of  50,000  cu.  ft.  of  air 
in  this  mine,  in  two  equal  parts. 

Solution. — The  first  step  is  to  calculate  the  value  1/XUZ  =  s/a3  for 
each  sectional  division ;  thus 

Main  intake,  7X10  ft.,  3000  ft.  long:  a=  70  sq.  ft.;  s  =  102,000  sq.  ft. 
Cross-entries  5X12  ft.,  6000  ft.  long :  a  =  120  sq.  ft. ;  s  =  204,000  sq.  ft. 
Main  returns,  7X12  ft.,  3000  ft.  long:  a  =  168  sq.  ft.;  s  =228,000  sq.  ft. 

Substituting  these  values  in  the  formula  for  finding  the  part 
potential  factor  for  each  section, 


Two  splits, 
Two  main  returns, 

Xi3          70  X  70  X  70 
1                  204,000 

=  0.1181 

Xf       120  X  120  X  120 
1                 228,000 

V   3            1  AQ     \S    1  «C     \s    1  no 

VJ.VJtOV/ 

Potential  factor  for  entire  mine   l/X03 0.4635 

For  the  horsepower  and  water  gage,  we  have 

kQ*       1        0.00000002  X  50,0003    x 
H  =  f  =  33,000  -  X 


=  kQ^  J_  =  0.00000002  X  50, OOP2 
W'9'  ~  5.2  X03  ~  5.2 

TANDEM  CIRCULATIONS 

Summation  of  Potentials. — When  an  air  current  passes  in 
succession  through  two  or  more  airways  of  different  section, 
the  total  unit  pressure  (Ib.  per  sq.  ft.)  due  to  the  circulation  is 
equal  to  the  sum  of  the  unit  pressures  of  the  several  sections. 
The  arrangement,  in  this  case,  may  be  described  as  "tandem." 

Likewise,  in  a  tandem  circulation,  the  total  power  on  the 
air  (ft.-lb.  per  min.)  producing  the  circulation  is  equal  to  the 
sum  of  the  powers  absorbed  in  the  several  sections  through 
which  the  current  passes. 

Indicating  the  potentials  of  the  respective  sections  of  the 


THEORY  OF  VENTILATION  215 

air-course  in  a  tandem  circulation  by  Xi,  X2,  X3,  etc.;  and  the 
corresponding  unit  pressures  and  powers  on  the  air  by  pi,  p2, 
p3,  etc.;  and  MI,  M2,  M3,  etc.,  respectively,  remembering  that  the 
square  of  the  pressure  potential  is  equal  to  the  cube  of  the 
power  potential,  as  expressed  by  the  formula 


we  can  write  the  following: 

For  tandem  circulations,  calling  the  general  mine  pressure 
po  and  the  total  power  on  the  air  UQ. 

Mine  pressure,     p(}  =  Q2  l^-r  +  -^-    +  etc 

\A  "i        A     2 


=  Q2  (w~  +  vT"  +  etc') 
\A°tti        A3u2  / 


or  7>o 

\tti  u2 

These  formulas  may  be  written  more  simply  by  indicating 
the  summation  of  the  potential  factors  by  the  character  £; 
thus, 

Mine  pressure,  pQ  =  Q~  £  (-«y) 

\A     i 

In  like  manner,  the  total  power  on  the  air  or  power  pro- 
ducing tandem  circulation  in  a  mine  is  expressed  by  the 
formula, 

Power  on  the  air,    UQ  =  Q3  (  -^g~~  H~  ^T 

\A  ui        A 


or  u0  =  Q8        --  h 


—  h  etc.) 

2  ' 


These  formulas  may  be  expressed  by  indicating  the  sum- 
mation of  the  potential  factors  by  2,  as  before;  thus, 

Power  on  the  air  u0  =  Qs  £ 


In  a  tandem  circulation,  if  desired,   the  general  mine  po- 


216  MINE  GASES  AND  VENTILATION 

tentials  for  power  (Xu0)  and  for  pressure  (Xp0)  can  be  calcu- 
lated by  the  formulas 

Xua  =  -T7  =;  and  Xvo  = 

"•*'  3    /     _  -.  /     TT-rt          \     *  " 


To  illustrate  the  formulas  that  apply  to  a  tandem  circu- 
lation where  a  single  air  current  is  carried  continuously  through 
shafts  and  airways  of  different  size  or  cross-section,  assume 
the  following  mine  is  passing  30,000  cu.  ft.  of  air  in  a  single 
undivided  current: 

1.  Downcast  shaft  ................     8  X  12  ft.,    600  ft.  deep 

2.  Main  road  and  return,  each.  ____     6  X  10  ft.,  1200  ft.  long 

3.  Cross-tunnel  and  return,  each.  .  .     6X8  ft.,    200  ft.  long 

4.  Upper  seam  and  return,  each.  ...     5  X  14  ft.,  2000  ft.  long 

5.  Upcast  shaft  ..................  10  X  10  ft.,  225'0  ft.  deep 

The  sectional  areas  are  96,  60,  48,  70  and  100  sq.  ft.;  and 
the  rubbing  surfaces,  24,000,  76,800,  11,200,  152,000  and 
90,000  sq.  ft.,  respectively. 


Part  potential  factors,     -!-,  =  -.  -•  -^T  =  "  =  °-0271 

.AM        a      .A  i         yo 


703 
90,000 


152,000  = 

=  0.0900 


oo8 


Potential  factors  for  entire  mine,  2  (ip-J  =  1-0170 

Mine  part       %      =  ^  =  =  0  9944 

potentials,  "  \/S(l/^u3)  "    ^1.0170 


Xpo  =  -    — L =      ,  l          =  0.9916 

vsa/Xp2)     v  i.oi7o 

fcQ2        0.00000002  X  30,0002      1Q  Q 
Pressure,  p-  =  ^3      -  -        -  -  =  18.3 

u<jy±  Ib.  per  sq.ft. 


THEORY  OF  VENTILATION  217 

Water  gage,   w.g.  =  p/5.2  =  18.3  -f-  5.2  =  3.5  in. 

Power  on  _  fcQ3  _  0.00000002  X  3Q,0003 

the  air,  =  X*uo~  0.99443  fl 

„  u  549,000  . 

Horsepower,      ff  ==      -         «  -  -  16.6  ftp. 


Example.  —  A  shaft  mine  has  been  opened  on  the  triple-entry  system. 
The  downcast  and  upcast  shafts  are  each  600  ft.  deep  and  8  X  20  ft.  in 
section.  The  main  headings  have  been  driven  a  distance  of  2000  ft. 
from  the  shaft  bottom.  The  center  one  of  these  headings  is  the  intake 
and  is  7  X  14  ft.  in  section,  while  the  two  side  headings  are  the  return 
airways  for  the  respective  sides  of  the  mine  and  are  each  6  X  12  ft.  in 
section.  On  each  side  of  the  main  headings,  cross-headings,  6  X  10  ft.  in 
section,  have  been  driven  500  ft.,  including  the  return  in  each. 

If  the  intake  air  divides  at  the  face  of  the  main  heading  and  equal 
currents  ventilate  the  two  sides  of  the  mine,  what  power  on  the  air  will 
be  required  to  circulate  a  total  of  60,000  cu.  ft.  per  min.  in  this  mine,  and 
what  water  gage  will  be  produced  in  the  fan  drift? 

Solution.  —  The  first  step  is  to  calculate  the  potential  values  of  the 
two  shafts,  main  intake,  two  cross-headings  and  two  return  airways,  as 
follows,  remembering  that  these  being  equal  splits,  it  is  only  necessary 
to  double  the  potentials  of  the  cross-headings  and  return  airways  by  tak- 
ing twice  the  sectional  area,  in  each  case: 

Shafts,                           8X20  ft.,    600ft.;  a  =160  sq.ft.;  s=     67,200  sq.  ft. 

Main  intake,                7  X  14  ft.,  2000  ft.;  a  -     98'  sq.  ft.;  s  =    84,000  sq.  ft. 

Two  cross-headings,  6  X  10  ft.,    500  ft.;  2o  =  120  sq.  ft.;  s  ==     32,000  sq.  ft. 

Two  return  airways,  6  X  12  ft.,  2000  ft.;  2a  =  144  sq.  ft.;  s  =  144,000  sq.  ft 

The  part  potential  factors  are  then  as  follows,  omitting  k 

- 


Main  intake,  ~  =  -3         =  ^||^     =0.0892 

.A  u  CL  aO 

Two  cross-headings,  -  ~       =  --     =  0.0185 


Two  return  airways,     j^—s  =  .     .3    =  ""1443"" 


Sum  of  potential  factors,  2  h^    .....  .......  0.1723 

The  horsepower  on  the  air  in  the  fan  drift,  in  this  case,  is  found  by  sub- 
stituting this  general  potential  factor,  in  the  formula  for  finding  the  power 
in  a  tandem  circulation;  thus, 

kQ3     ^/   1  \       0.00000002  X  60,0003  X  0.1723 
H  *"  3^000  SfeV  =  —33,000  =  22  55  hp' 


218  MINE  GASES  AND  VENTILATION 

The  water  gage,  in  the  fan  drift,  due  to  this  circulation,  can  be  calcu- 
lated in  like  manner,  independently,  from  the  same  general  potential 
factor,  by  substituting  the  same  in  the  formula  for  finding  the  unit  pres- 
sure and  water  gage  in  a  tandem  circulation;  thus, 

0.00000002  X  60,0002  X  0.1723 

-5±~  -  -  2'38+  **• 

The  same  result  is  obtained  when  the  water  gage  is  calcu- 
lated from  the  power  and  the  quantity  of  air  in  circulation. 

u         22.55  X  33,000 

~   ~~  H' 


SPLITTING  THE  AIR  CURRENT 

Early  Practice,  Coursing  the  Air. — In  the  early  practice 
of  mine  ventilation,  the  method  commonly  adopted  was  that 
known  as  "  coursing  the  air."  In  this  method  the  air  was 
conducted  throughout  the  mine  in  one  continuous  current, 
from  the  intake  opening  to  the  point  where  it  was  again 
discharged  into  the  atmosphere. 

Single  Current  Not  Adequate. — Experience  has  shown, 
however,  that  a  single  air  current  is  not  adapted  to  the  ven- 
tilation of  a  large  mine,  for  many  reasons.  As  a  mine  is 
developed  and  the  workings  extended,  more  men  are  employed 
and  greater  quantities  of  air  are  required  to  ventilate  the 
mine  and  dilute  and  carry  away  the  gases  generated. 

Need  of  Dividing  the  Air  Current. — The  division  of  the  air 
into  two  or  more  currents  provides  separate  ventilation  dis- 
tricts in  the  mine  and  brings  the  ventilation  under  better 
control,  since  the  quantity  of  air  can  then  be  proportioned 
to  the  requirements  in  each  district 

A  larger  volume  of  air  can  be  circulated  by  the  same  power, 
and  the  velocity  of  the  current  is  kept  low. 

The  smoke  and  gases  generated  in  one  section  of  the  mine 
are  not  carried  by  the  current  into  another  section,  but  pass 
directly  into  the  main  return  airway  and  are  conducted  out 
of  the  mine. 

A  local  explosion  of  gas  or  dust,  in  one  portion  of  the  mine, 
is  not  as  liable  to  extend  throughout  the  mine. 


THEORY  OF  VENTILATION  219 

Method  of  Splitting  the  Air-current. — Whenever  two  or 
more  passages  or  airways  are  provided  by  which  the  air 
current  can  travel  in  passing  through  the  mine,  the  air  will 
always  divide  between  them  in  proportion  to  their  several 
potential  values.  Hence,  all  that  is  required  to  split  an  air- 
current  is  to  provide  two  or  more  separate  routes  for  its 
pa'ssage.  Each  separate  current  is  called  an  "air  split"  or 
simply  a  " split." 

Natural  Splitting. — When  all  the  airways  are  open  to  the 
free  passage  of  the  air-current  through  them,  the  air  divides 
naturally  between  them,  each  airway  or  split  taking  a  quan- 
tity of  air  in  proportion  to  its  potential  value.  In  other 
words,  the  potential  of  the  airway  is  an  index  of  the  quantity 
of  air  that  airway  will  pass,  in  natural  splitting. 

Proportionate  Splitting. — When  any  other  division  of  the 
air  is  desired  than  the  natural  division,  it  is  necessary  to 
introduce  regulators  in  one  or  more  of  the  airways  so  as  to 
obstruct  the  flow  in  those  splits  that  naturally  take  more 
than  the  desired  proportion,  and  thereby  increase  the  quantity 
passing  in  the  other  airways  till  the  desired  proportion  is 
reached. 

Primary  and  Secondary  Splits. — -A  branch  or  split  off  the 
main  air  current  is  called  a  "  primary  split."  If  a  primary 
air  split  be  again  divided,  the  result  is  a  " secondary  split." 
When  the  air  current  is  equally  divided  between  two  or  more 
airways  the  splits  are  said  to  be  "equal;"  but  when  each 
airway  passes  a  different  volume  of  air  the  splits  are 
"unequal." 

Increase  of  Quantity  Due  to  Splitting. — The  quantity  of  air 
in  circulation  is  proportional  to  the  general  mine  poten- 
tial. In  other  words,  the  quantity  ratio  is  always  equal  to  the 
mine-potential  ratio;  the  power  potential  being  used  for  a 
constant  power,  and  the  pressure  potential  for  a  constant 
pressure;  always  remembering,  however,  that  the  cube  of 
the  power  potential  is  equal  to  the  square  of  the  pressure 
potential.  Denoting  the  original  quantity  of  air  in  cir- 
culation, by  Qi  and  the  original  mine  potentials  for  power 
and  pressure  by  Xui  and  Xpi,  respectively;  and  designating 


220  MINE  GASES  AND  VENTILATION 

these  factors  after  splitting,  by  Q2)  Xu2  and  Xp2,  respectively, 
we  have  the  following  formulas: 

~  Xu2        ~         -3  \ /Xn$ 
Power  constant,     Q2  =  Qi  -^— ;  or  Q2  =  Qi 


3 

Pressure  constant,Q2  =  Qi  ^^;  or  Q2  =  Qi 

Api  \   \^\ui/ 

An  illustration  of  the  use  of  these  formulas  is  to  be  found 
in  the  solution  of  the  example  given  under  Secondary  Splitting. 
In  that  example  (p.  242),  the  power  on  the  air  remained 
constant  before  and  after  splitting  the  current.  The  pressure 
potential  was  used,  which  before  splitting  was  Xpi  =  0.6708, 
and  after  splitting  Xp2  =  0.8554: 


Hence,  Q2  =  Qi^/(fj)  '    =  120,000^  (gg)  *  =  141,100 

cu.  ft.  per  min. 

NATURAL  DIVISION  OF  AIR 

In  all  splitting  calculations,  it  is  assumed  that  the  unit 
pressure  (Ib.  per  sq.  ft.)  is  the  same  at  the  mouth  of  each 
split  starting  from  the  same  point.  Therefore,  writing  the  for- 
mula for  unit  pressure, 

kloq2        ,    9      p/a3\ 

P  —  —  11  and  q   =  T  (r-J 

a3  k  \lo  I 

Then,  since  p  and  k  are  both  constant,  qz  varies  as  a3/lo 

/• 

and  q  varies  as  «A/T- 

This  expression,  as  previously  explained  is  the  pressure  poten- 
tial of  the  airway.  It  must  be  remembered  that  the  square 
of  the  pressure  potential  (Xp)  is  equal  to  the  cube  of  the  power 
potential  (Xu);  thus, 


It  is  the  pressure  potential  that  is  always  used  in  splitting 
calculations;  because,  as  stated  above,  the  unit  pressure  is  the 


THEORY  OF  VENTILATION  221 

same  for  all  splits  at  one  point.  The  calculation  of  the  quan- 
tity of  air  passing  in  any  one  of  two  or  more  splits  starting  from 
the  same  point  in  a  mine,  is  based  on  the  following  simple 
rule  : 

Rule.  —  The  ratio  of  the  quantity  of  air  passing  in  a  single 
split,  to  the  total  quantity  for  all  the  splits,  is  equal  to  the 
ratio  of  the  pressure  potential  of  that  split,  to  the  sum  of  the 
pressure  potentials  for  all  the  splits. 

Calling  the  quantities  passing  in  the  several  splits,  q\,  qz, 
q3,  etc.,  and  the  corresponding  split  potentials  Xi,  X^  X3,  etc.; 
the  total  quantity  of  air  in  circulation  in  all  the  splits  Q,  and 
indicating  the  sum  of  the  split  potentials  by  2X; 

Q  =  qi  +  q*  +  q-t  +  etc. 
and 

VX  =  Xi+  X2+  X3  +  etc. 

Then,  according  to  the  rule  given  above, 


Q   " 

The  work  of  calculation  is  much  simplified  and  shortened 
by  using  what  may  be  called  the  "  relative  potential"  values, 
instead  of  finding  the  actual  pressure  potential  for  each  split. 
This  is  only  possible  in  splitting  calculations,  where  the 
potentials  are  used  as  ratios,  and  the  value  of  the  ratio  is 
not  changed  by  the  cancellation  of  any  like  factors  in  all  the 
potentials. 

Relative  Potential  Values.  —  Whenever  the  potential  is 
used  as  a  ratio,  as  in  splitting  air  currents,  the  relative  values 
should  be  used.  These  are  calculated  from  the  lowest  relative 
values  for  the  areas,  perimeters  and  lengths  of  the  several 
airways  or  splits.  For  example,  if  the  areas  are  48,  60  and 
72  sq.  ft.,  the  lowest  relative  values,  canceling  the  common 
factor  12,  are  4,  5  and  6,  respectively  Likewise,  instead  of 
the  perimeters,  28,  32,  34;  use  the  lowest  relative  perimeters 
14,  16,  17,  canceling  the  common  factor  2  from  each. 

The  use  of  the  ''relative  potential'7  value,  in  all  calculations 
to  determine  the  natural  division  of  air  between  two  or  more 


222  MINE  GASES  AND  VENTILATION 

airways,  is  one  of  the  most  important  considerations  in  the 
saving  of  time  and  labor  and  avoiding  unnecessary  mul- 
tiplicity of  figures,  which  increases  the  opportunities  for 
error  and  yields  less  accurate  results.  An  example  or  two 
will  serve  to  make  this  fact  plain. 

Summation  of  Split  Potentials. — The  circulation  of  air  in 
two  or  more  splits  or  currents,  in  a  mine,  differs  from  a  tan- 
dem circulation  in  the  fact  that  the  same  unit  pressure  circu- 
lates the  air  in  each  and  all  the  splits,  which  are  thus  separate 
currents  moved  by  one  pressure;  while  in  a  tandem  circula- 
tion one  continuous  current  passes  in  succession  through 
different  airways  or  sections  of  the  mine. 

While  in  a  tandem  circulation  the  mine  pressure  is  equal 
to  the  sum  of  the  pressures  for  the  several  sections  through 
which  the  current  passes;  and,  likewise,  the  total  power  for 
the  mine  is  equal  to  the  sum  of  the  powers  absorbed  in  the 
sections;  in  a  split  circulation,  the  total  power  for  the  mine 
is  equal  to  the  sum  of  the  powers  absorbed  in  the  splits,  but 
there  is  but  one  pressure,  which  is  the  same  for  all  the 
splits  starting  from  the  same  point  in  the  mine.  As  before, 
indicate  the  several  split  pressure  potentials  by  Xpi,  Xp2, 
Xp3,  'etc.;  the  corresponding  powers  on  the  air  by  MI,  u2,  u3, 
etc.;  and  the  total  power  on  the  air  by  MO,  remembering  that 
it  is  necessary,  in  all  splitting  calculations,  to  use  the  pressure 
potential, which  has  the  value 


The  work  is  simplified  by  using  the  part  potential  value, 
as  previously  stated,  omitting  k  when  finding  the  potential 
values  and  multiplying  the  final  result  by  that  coefficient. 

The  following  shows  the  development  of  the  formulas  for 
the  summation  of  the  potentials  in  split  circulations  where 
the  splits  all  start  from  one  point  in  the  mine : 

u0=  MI+  u2  +  etc.  (1) 

But,  MI  =  JT-;  u2  =  -£-;  etc.  (2) 

A   pi  A   p2 


THEORY  OF  VENTILATION  223 

By  the  principle  of  splitting  air  currents, 


Combining  equations  2  and  3  and  simplifying, 


Finally,  substituting  these  values   (4)  in  equation   1,  and 
factoring, 


From  Equation  5  is  obtained  the  formula  for  calculating 
the  horsepower  on  the  air  at  the  point  of  split,  by  the  sum- 
mation of  the  part  pressure  split  potentials  : 

/cO3 
Horsepower  on  the  air,       H  =  - 


The  formula  for  calculating  the  water  gage,  in  like  manner,  is 

kQ2 
Water  gage,      _  „,.„.=___  (7) 

Equal  Splits.  —  When  an  air  current  is  divided  naturally  be- 
tween two  or  more  equal  splits,  the  calculation  of  the  mine 
potentials,  velocity,  pressure,  power,  etc.,  is  the  same  as  for 
a  single  undivided  current,  except  that  the  sectional  area  (a) 
of  the  airways  must  be  multiplied  by  the  number  of  splits  (n) 
to  obtain  the  total  area  of  passage  (no). 

To  illustrate  the  application  of  the  formulas  in  this  case, 
assume  an  air  current  of  60,000  cu.  ft.  of  air  is  circulated  in 
three  equal  splits,  the  size  and  total  length  of  the  airways, 
including  the  returns  being  5X8  ft.  and  10,000  ft.  long. 

Q         60,000 
Velocity,  v  =  -'-  =         '  =  500  ft.  per  mm. 

Hd          o^O   /\  oj 

Mine  part        %    =   na    _    3(5  X  8)    _ 
potentials,       u       ^/~g       ^260,000 


v  /""*        ion    /      l^u       _  o  K7Q 

Z.^IUK/-     =  120->26p>06-2-578 

,.^         0.00000002  X  60,0002 
Pressure,  p  =  -£-  =  -*****-         ~  =  10-83 

to.  per  sq.  ft. 


224  MINE  GASES  AND  VENTILATION 

Water  gage,    w.g.  =  p/5.2  =  10.83  -5-  5.2  =  2.08  in. 

Power  on 

the  air,  _  kQ3  _  0.00000002  X  60,0003 

u  —  -^ — 3  —  —  — ^  003 —  —  ooO,OOu 

*  '  ft.-lb.  per  min. 

u  650,000 

Horsepower,      H  --  ^^  --  -^^  --  19.7  hp. 

Unequal  Splits. — To  illustrate  the  formulas  used  in  the  cal- 
culation of  the  natural  division  of  an  air  current  between 
two  or  more  airways  and  the  pressure  and  power  on  the  air, 
assume  a  current  of  75,000  cu.  ft.  per  min.  is  passing  in  the 
following  three  splits,  starting  from  the  same  point  of  the 
main  airway  or  at  or  near  the  intake  opening.  The  lengths 
given  for  the  several  splits  include  the  return,  in  each  case; 
and  the  pressure  and  power  are  for  the  circulation  in  the 
splits  only. 

Split  A,  6  X  10  ft. ;  2000  ft.  long ;  a  =  60  sq.  ft. ;  o  =  32  f t. ;  Z  =  2000  ft. 
Split5,  6  X  8ft.;  1500ft,  long;  a  =  48 sq.ft.;  o  =  28ft.;  I  =  1500ft, 
Split  C,  4  X  12  ft. ;  2500  ft.  long;  a  =  48  sq.  ft. ;  o  =  32  ft. ;  I  =  2500  ft. 

The  lowest  relative  values  are  as  follows:  Areas,  5,  4,  4;  pe- 
rimeters, 8,  7,  8;  lengths,  4,  3,  5. 

Relative  split  pressure  potentials, 


Sum  of  potentials,     2XP  ...........................    4.987 

Natural  division  of  air  current, 

X  75'00°  =  29'72°  ™'  fL 
X  75,000  =  26,260  CM.  ft. 

=  19,020  cu.  ft. 


Total  circulation,  Q  ................      75,000  cw.  ft. 


THEORY  OF  VENTILATION  225 

To  calculate  the  pressure  and  power  of  the  circulation,  it 
is  necessary  to  employ  the  part-potential  values,  instead  of  the 
relative  values;  thus, 

Part  potential  values, 


48 


-^pc  —  4oA  /^^^^  .  .  «^. —   1.1/D 


48 

2500X32 
General  part  potential  for  splits,   SXP 4.636 

kQ2         7  /    Q  \ 2 
Pressure,  p  —       -^  .2  =  k (     „  j 

p.  =  0.00000002  (-^03°60)  2  =  5.2  Ib.  per  sq.  ft. 

Horsepower  on  the  air, 

feQ3  0.00000002  X  75,OOQ3 

-  oo  ™«/  v,  v  N9.  -       33^00  X  4.6362  P* 


EXAMPLES  IN  NATURAL  DIVISION 

Example. — An  air  current  of  100,000  cu.  ft.  per  min.  is  divided  at  the 
foot  of  the  downcast  shaft,  between  the  following  four  air-courses  or 
splits,  thereby  providing  two  separate  ventilation  districts  on  each  side  of 
the  shaft : 

Split  A,  8  X  12  ft.,  6000  ft.  long 

Split  5,  6  X  20  ft.,  12,000  ft.  long 

Split  C,  6  X  12  ft.,  8000  ft.  long 

Split  D,  4X6  ft.,  1000  ft.  long 

All  the  splits  are  open  to  the  free  passage  of  the  air,  no  regulators 
being  used,  (a)  Find  the  natural  division  of  the  main  air  current  or  the 
quantity  of  air  passing  in  each  split.  (6)  What  is  the  pressure  due  to  this 
circulation?  (c)  What  is  the  horsepower  on  the  air? 

Solution. — (a)  The  first  step  is  to  calculate  the  relative  pressure  poten- 
tial for  each  of  the  four  air  splits.  The  area,  perimeter  and  length  of 
each  airway  are  as  follows: 


Split  A, 

a 

=    96 

sq. 

ft.; 

0 

=  40ft.; 

I 

=    6,000 

Split  B, 

a 

=  120 

sq. 

ft.; 

o 

=  52 

ft.; 

I 

=  12,000 

Split  C, 

a 

=    72 

sq. 

ft.; 

o 

=  36 

ft.; 

I 

=    8,000 

Split  D, 

a 

=    24 

sq. 

ft.; 

0 

=  20 

ft.; 

I 

=     1,000 

15 

226  MINE  GASES  AND  VENTILATION 

Instead  of  using  these  full  values  as  when  finding  the  true  potential 
value  of  an  airway,  the  lowest  relative  values  for  the  areas,  perimeters 
and  lengths  are  used.  These  relative  values  are  obtained  by  canceling 
the  common  factors  in  the  areas,  perimeters  and  lengths  separately,  which 
gives  the  following  : 

Split  A,  a  =  4;  o  =  10;  /  =    6 

Split  B,  o  =  5;  o  =  13;  I  =  12 

Split  C,  a  =  3;  o  =    9;  I  =    8 

Split  Z>,  a  =  l;  o=5;  Z=l 


Split 


The  relative  split  potentials  are  then  found  as  follows  : 

4 


Split  D, 

Sum  of  relative  potentials  .......................   2  .  987 

Since  the  quantity  of  air  passing  in  each  split,  in  natural  division  is 
proportional  to  the  corresponding  potential,  the  quantity  ratio  is  equal  to 
the  potential  ratio,  which  is  true  also  for  the  sum  of  the  quantities  and 
the  sum  of  the  potentials.  Thus,  the  ratio  'of  the  quantity  (q)  passing 
in  any  split,  to  the  total  quantity  (Q)  in  circulation,  is  equal  to  the  ratio 
of  the  corresponding  split  pressure  potential  (Xp),  to  the  sum  of  all  the 
split  potentials 


Therefore,  substituting  the  relative  potential  values  just  found  in  this 
formula  gives  the  following  : 

1  0^*3 
Split  A,  qa  =  ^ggy  X  100,000  =  34,570  cu.  ft.  per  min. 

0  SQ^ 
Split  B,  qb  =  ^^  X  100,000  =  29,960  cu.  ft.  per  min. 


Split  C,  qe  =          7  X  100,000  =  20,500  cu.  ft.  per  min. 

^.9o7 

Split  D,  qd  =  ^^  X  100,000  =  14,970  cu.  ft.  per  min. 


Total  quantity 100,000  cu.  ft.  per  min. 


THEORY  OF  VENTILATION  227 

(6)  Since  the  pressure  is  the  same  for  all  the  splits,  it  can  be  calculated 
from  any  one  of  the  given  splits,  by  substituting  the  values  for  that 
split  in  the  formula 

=  kloq2 
a3 

Thus,  taking  split  A, 

0.00000002  X  6000  X  40  X  34,5702 
p  =  96  X  96  X  96"  =  6'48  ^  ^  Sq'  fL 

(c)  The  horsepower  on  the  air  in  the  main  entry,  or  the  horsepower 
producing  this  circulation  is,  then, 

Qp          100,000  X  6.48 
H  =  337)00  =          33,000    '       = 

As  an  illustration  of  the  usefulness  of  the  summation  of 
potential  values,  we  give  below  the  calculation  of  the  horse- 
power on  the  air,  unit  pressure  and  water  gage  developed  in 
the  circulation  of  100,000  cu.  ft.  of  air  per  minute,  in  four 
splits,  previously  calculated  by  the  usual  method  in  the  last 
example,  where  it  was  necessary,  first,  to  find  the  natural  divi- 
sion of  the  air. 

Example. — An  air  current  of  100,000  cu.  ft.  per  ruin,  is  divided,  at  the 
foot  of  the  downcast  shaft,  between  the  following  four  splits: 

Split  A,  8  X  12  ft.,    6,000  ft.,  long;  a  =  96  sq.  ft.;  s  =  240,000  sq.  ft. 

Split  B,  6  X  20ft.,  12,000  ft.,  long;  a  =  120  sq.  ft. ;  s  =   624,000  sq.  ft. 

Split  C,  6  X  12  ft.,     8,000  ft.,  long;  a  =  72  sq.  f t. ;  s  =   288,000  sq.  ft. 

Split  D,  4  X     6ft.,     1,000  ft.,  long;  a  =  24  sq.  f  t. ;  s  =     20,000  sq.  ft. 

Calculate  the  horsepower  on  the  air,  unit  pressure  and  water  gage 
concerned  in  producing  this  circulation,  using  the  part  potential  values 
and  employing  the  method  by  summation  of  potentials;  no  regulators 
being  used  in  the  mine,  but  the  division  of  air  being  natural. 

Solution. — The  part  potential  values  for  the  several  splits  are  as  follows: 


XPI  =  a\l-  =       96\/0^  ^     =  1.920 


120 


r~i2 

Split  U,      Xp,    -  12°  \62p5a    =  L664 


Split  C,      Xp3    =  72X^7^     =1-138 


Split  D,      Xpt    - 

Sum  of  part  pressure  potentials  (2ZP)  5.553 


228  MINE  GASES  AND  VENTILATION 

Substituting  this  value  for  SZP,  in  the  formulas  for  finding  the  horse- 
power on  the  air  and  water  gage,  in  natural  splitting, 

0.00000002  X  100,0003 
Horsepower  on  air,       H  = 33>0oo  x  5.5532         =  19-6  hp 

0.00000002  X  100,0002 
Unit  pressure,  p  =  -          — -  -P.»2 —        -  =6.48  Ib.  per  sq.  ft. 

0.00000002  X|100,0002 
Water  gage,  w.g.  =  -         5.2  x  5.5532  =  1-24  in. 

In  natural  splitting  or  when  no  regulators  are  employed 
the  general  mine  potential  is  always  equal  to  the  sum  of  the 
several  split  potentials,  which  is  true  for  either  power  or 
pressure. 

General  Mine  Potential. — The  power  potential  for  the 
combined  splits  can  be  calculated  from  the  total  quantity  of 
air  in  circulation  and  the  resulting  pressure,  using  the 
formula 

02 

X 3M  =  — ;  or  AM  = 
P 

Example. — What  is  the  general  power  potential  for  all  the  splits  com- 
bined, in  the  example  given  above,  where  100,000  cu.  ft.  of  air  was  circu- 
lated under  a  pressure  of  6.48  Ib.  per  sq.  ft.? 

Solution. — The  general  power  potential  for  these  combined  splits  is 

3  |Q*  3  /100,0002 

Mine  power  potential,    AM  =\—  =  \/ — TTTT; —  =  H55 

\  p         \     6.48 

Example. — An  air  current  of  60,000  cu.  ft.  per  min.  is  passing  in  an 
airway  8  X  10  ft.  in  section,  to  a  point  1500  ft.  distant  from  the  foot  of 
the  downcast  shaft,  where  it  divides  naturally  between  the  following 
four  airways  or  splits: 

Split  A,  5  X  6  ft.,  900  ft.  long 

Split  B,  6X6  ft.,  825  ft.  long 

Split  C,  4  X  6  ft.,  840  ft.  long 

Split  D,  4X5  ft.,  720  ft.  long 

What  is  the  quantity  of  air  passing  in  each  split;  and  what  will  be  the 
water-gage  reading  for  the  entire  mine  and  power  on  the  air,  at  the  foot 
of  the  downcast  shaft?- 

Solution. — Since  the  water  gage  is  required  in  this  case,  the  relative 
potential  values  cannot  be  used;  but,  instead,  the  part  potential  value 
(omitting  ft)  is  found  for  the  main  airway  and  for  each  split  separately; 


THEORY  OF  VENTILATION  229 

thus,  taking  the  length  of  the  main  airway  including  the    return  as 
2X  1500  =  3000  ft.: 


Main 
Split 
Split 
Split 
Split 

airway, 
A, 

c, 

A 

a 

a 
a 
a 
a 

o  =  36;  I  = 

3000; 
900; 
825; 
840; 
720; 

Xl 

xa 
xb 
xc 
xd 

=  80 

J 

80 

=  2.177 
=  1.168 

Of). 

\3000  X  36 

J 

30 

—  OU, 

=  36; 
=  24; 
=  20; 

n  _  04.  /  _ 

\900 

X 

22 

J 

36 

U            .£<*,     £, 

n        90-7 

—  94 

\825 

X 

24 

0  Q07 

J 

24 

o  =  18;  Z  - 

90 

\840 

X 

20 

=  0.786 

J 

20 

\720 

X 

IS 

The  general  split  potential  (XQ)  is  equal  to  the  sum  of  the  potentials 
for  the  four  splits;  thus, 

XQ  =  ZXabcd  =  4.392 

The  quantity  of  air  that  will  pass  in  each  of  these  splits  is  proportional 
to  the  corresponding  split  potential,  assuming  that  no  regulators  are 
employed  but  all  the  airways  are  free  and  unobstructed.  The  natural 
division  of  the  air  between  the  four  splits  is  therefore  calculated  in  the 
usual  manner,  as  follows: 

.1.168 


Split 
Split 
Split 
Split 

A, 
B, 

c, 

D, 

9* 

Qb 
Qc 

=  60,000^^  =  15,950  cu. 
=  60,000^—^4=  =20,920  cu. 
=  60,000^000  =_12,390  cu. 
60  000°*786  —  10  740  ni 

ft. 

ft. 
ft. 
ft. 

per 
per 
per 
per 

min. 
min. 
min. 
min. 

-    Ou,UUU.    QOO  '•"-"    -'•U,<itU  Git. 

Total  circulation  60,000  cu.  ft.  per  min. 

In  order  to  find  the  water-gage  reading  at  the  foot  of  the 
downcast  shaft,  for  this  circulation,  it  is  necessary  to  cal- 
culate the  general  mine  potential  Xp  by  combining,  in  tan- 
dem, the  main-airway  potential  (Xi)  and  the  general  split 
potential  (X0)  previously  found,  using  the  formula  (p.  215). 

Mine  water  gage,  w.g.  =  ^  s  \X^* 

Substituting  the  values  of  the  potential  factors  previously  found. 
.Main  airway,  ^7-  =  ^  1772  =  0-2109 

Split  section,  -^-  =  T~oo2  =  0.0518 


oqo2 


Sum  of  values,  S(1/AV)  0.2627 


230  MINE  GASES  AND  VENTILATION 

Finally,  substituting  this  value  in  the  above  formula  for  finding  the 
mine  water  gage, 

0.00000002  X  60,0002  x  0.2627 
w.g.  =  -  52  ~   =  3.64  in. 

In  like  manner,  the  power  on  the  air,  at  the  foot,  of  the  shaft  is  calcu- 
lated by  the  formula 


JcQ^_     (  1  \  _  0.00000002  X 
~  3,3,000      \XV-]  ~  33,000 


PROPORTIONATE  DIVISION  OF  AIR 

Every  large  and  well  managed  mine  is,  now,  divided  into 
two  or  more  separate  ventilation  districts.  The  natural  divi- 
sion of  the  air  current  between  these  several  districts  is  not 
generally  in  proportion  to  their  respective  needs. 

The  longer  entries,  working  more  men  and  requiring  the 
most  air  for  their  ventilation  are  the  ones  that  have  the 
greater  resisting  power  and,  as  a  result,  receive  a  lesser 
proportion  of  the  air,  in  natural  division;  while,  on  the  other 
hand,  the  shorter  air-courses  where  fewer  men  are  working 
and  less  air  is  required,  have  a  smaller  resisting  power  and 
naturally  pass  the  larger  quantity  of  air. 

To  Regulate  the  Air. — In  order  to  overcome  these  natural 
conditions,  in  mine  ventilation,  and  divide  the  main  air  cur- 
rent so  as  to  give  each  district  of  the  mine  the  required  pro- 
portion of  air,  it  is  necessary  to  employ  some  means  that  will 
produce  this  result. 

Two  methods  have  been  used  to  divide  the  air  proportion- 
ately; they  are  as  follows: 

1.  The  flow  of  air  is  obstructed  in  those  airways  that  take 
naturally  more  than  the  desired  porportion. 

2.  The  power  on  the  air,  at  the  mouth  of  each  split,  is 
proportioned  to  the  work  to  be  performed  in  that  split. 

The  former  of  these  two  methods  has  been  in  common  use 
for  many  years;  the  latter  was  suggested  (Mine  Ventilation, 
Beard,  1894,  p.  93)  as  an  improvement  and  has  been  put  in 
use  since  in  many  mines  where  practical  considerations  would 
permit. 


THEORY  OF  VENTILATION 


231 


The  Box  Regulator. — This  form  of  regulator  is  shown  in 
Fig.  32  (a),  and  consists  of  a  brattice  built  in  the  return  airway 
or  haulway.  As  shown  in  the  figure,  an  opening  is  provided 
in  the  brattice  and  a  sliding  shutter  is  used  to  regulate  the 
size  of  the  opening  so  as  to  control  the  flow  of  air  in  that 
airway  or  split.  If  more  air  is  needed  the  shutter. is  pushed 
back  so  as  to  enlarge  the  opening ;  or  the  shutter  can  be  partially 
closed  to  decrease  the  quantity  of  air  passing  in  the  split. 

The  Door  Regulator. — Wherever  the  conditions  will  permit 
this  form  of  regulator  to  be  employed  it  will  be  found  an  im- 
provement over  the  common  "box  regulator,"  just  described. 

As  shown  in  Fig.  32  (6) ,  the  door  regulator  consists  of  a  door 
hung  at  the  mouth  of  an  entry  or  split  and  swung  into  the 


FIG.  32. 


wind.  The  door  should  be  arranged  so  that  it  will  fall  natur- 
ally against  a  set-stop,  and  when  not  in  use  will  assume  a  posi- 
tion whereby  the  air  current  will  be  divided  in  the  desired 
proportion,  between  the  two  airways  or  splits. 

Effect  of  Regulator. — Any  regulation  of  the  air  current  in 
a  mine,  to  accomplish  a  distribution  of  air  other  than  what 
is  natural,  causes  an  increase  of  both  the  power  producing 
the  circulation  and  the  resulting  pressure  or  water  gage. 
This  is  true  in  every  case,  whatever  form  of  regulator  is 
employed,  provided  the  total  quantity  of  air  in  circulation  is 
not  decreased.  The  reason  *that  an  increase  of  power  is 
necessary  in  proportionate  splitting,  is  that  an  increase  in  the 
circulation  in  any  split  causes  a  corresponding  increase  in 
pressure;  and  this  pressure  is  the  same  for  all  splits  starting 


232  MINE  GASES  AND  VENTILATION 

from  the  same  point  in  the  mine.  To  circulate  the  same  quan- 
tity of  air  against  this  higher  pressure  requires  a  correspond- 
ing increase  of  power. 

Illustration. — Let  it  be  required  to  find  the  horsepower  and  the  pres- 
sure per  square  foot,  in  the  following  distribution  of  the  air  current  be- 
tween the  following  four  splits;  the  natural  distribution  of  air,  as  previ- 
ously calculated  (p.  225),  being  repeated  here,  for  sake  of  comparison: 

Nat.  div.  Reqd.  div. 

(cu.  ft.  p.  m.)  (cu.  ft.  p.  m.) 

Split  A,             8  X  12  ft.,    6,000  ft.  long,                    34,570  20,000 

Split  B,             6  X  20  ft.,  12,000  ft.  long,                    29,960  40,000 

Split  C,             6  X  12  ft.,    8,000  ft.  long,                    20,500  30,000 

Split  D,             4  X     6  ft.,     1,000  ft.  long,                    14,970  10,000 

Total  circulation,                                                          100,000  100,000 

Solution. — The  first  step  is  to  calculate  the  natural  pressure  for  each 
split  when  passing  the  required  quantity  of  air  per  minute,  by  substitut- 
ing the  following  values  for  the  area,  perimeter  and  length  of  each  split, 
in  the  formula  for  finding  the  unit  pressure: 


Split  A,  a  =  96  sq.  ft.  o  =  40  ft. 

Split  B,  a  =  120  sq.  ft.  o  =  52  ft. 

Split  C,  a  =  72  sq.  ft.  o  =  36  ft. 

Split  D,  a  =  24  sq.  ft.  o  =  20  ft. 


I  =     6,000ft. 

I  =   12,000  ft. 

I  =     8,000ft. 

I  =     1,000ft. 


The  natural  pressure  in  each  split  is  then  calculated  as  follows : 

0.00000002  X  6000  X  40  X  20,0002 
Split  A,  p  =  -  96  x  96  x  96  =  2.17  Ib.   per  *q.  ft. 

0.00000002  X  12,000  X  52  X  40,0002 
Spht  B,  p  =  -  12Q  X  120  X  120  ~  =  1L55  lb'  per  «*  *' 

0.00000002  X  8000  X  36  X  30,0002 
Split  C,  p  = 72  X  72  X  72 =    3'89  l     per  sq'  &' 

0.00000002  X  1000  X  20  X  10,0002 
Split  D,  p  =  24  X  24  X  24 =  2<98  *'  per  sq'  fi' 

The  highest  natural  pressure  is  developed  in  Split  C,  in  the  required 
distribution  of  air,  and  that  is,  therefore,  the  "open"  or  "free"  split, 
regulators  being  necessary  in  each  of  the  other  splits,  to  raise  the  pres- 
sure to  the  same  amount. 

The  horsepower  producing  this  circulation  is  then 

100,000  X  13.89 

33,000  42'09  hp' 

Pressure  Due  to  Box  Regulator. — The  primary  effect  of  this 
regulator  is  to  increase  the  pressure  on  its  intake  side,  by 


THEORY  OF  VENTILATION  233 

obstructing  the  flow  of  air  in  the  airway  or  split  that  it  con- 
trols. This  increase  of  ventilating  pressure  is  necessary 
to  accomplish  the  desired  increase  of  circulation  in  another 
airway,  which  remains  open  or  unobstructed  and  which,  for 
that  reason,  is  called  the  "free  split." 

The  increase  of  pressure  is  the  pressure  due  to  the  reg- 
ulator; and  is  equal  to  the  difference  between  the  natural 
pressure  of  the  free  split  and  that  of  the  split  in  which  the 
regulator  is  placed,  calculated  for  the  required  distribution 
of  air.  For  example,  in  the  illustration  previously  given,  the 
natural  pressure  required  to  circulate  30,000  cu.  ft.  of  air  in 
Split  C  was  13.89  Ib.  per  sq.  ft.,  while  that,  required  to  cir- 
culate 20,000  cu.  ft.  in  Split  A  was  only  2.17  Ib.  per  sq.  ft.  The 
pressure  due  to  the  regulator  in  Split  A  is,  therefore, 

13.89  -  2.17  =  11.72  Ib.  per  sq.  ft. 

Velocity  of  Air  Passing  Regulator. — The  velocity  of  the  air 
flowing  through  the  regulator  is  determined  by  the  difference 
of  pressure  on  its  two  sides  or  the  pressure  due  to  the  regulator. 
This  velocity  is  calculated  from  the  well  known  formula 

v  =  \/2gh 

In  the  case  of  a  regulator,  the  pressure  head  is  equal  to 
the  pressure  (pr)  due  to  the  regulator,  divided  by  the  weight 
of  1  cu.  ft.  of  air  (w  =  0.0766  Ib.);  and  taking  2g  -  2  X 
32.16  =  64.32  ft.  per  sec.,  the  theoretical  velocity  of  the  air 
due  to  this  pressure  is 


By  this  formula,  the  theoretical  velocity  corresponding  to 
the  pressure  due  to  the  regulator  in  Split  A  is 


v  =  29-V/H.72  =  99.28  ft.  per  sec. 

Quantity  Passing  Regulator. — Owing  to  the  vena  con- 
tract a,  at  the  opening  in  a  box  regulator,  the  effective  area 
of  the  opening  is  only  0.62  of  the  actual  area  A;  and  the 


234  MINE  GASES  AND  VENTILATION 

quantity  (Q),  in  cubic  feet  per  minute,  passing  through  the 
opening,  is 

Q  =  60(0.62At;)  =  37.2Av 
Or,  substituting  the  value  of  v,  as  given  above, 

Q  =  37.2  X 
Or,  since  p  =  5.2  w.g. 

Q  =  1078AV5.2ti>.0.=  say 

Area  of  Opening,  Box  Regulator.— The  area  of  the  opening 
required  to  pass  any  given  quantity  of  air,  in  splitting,  is 
found  by  solving  the  last  formula  given  above,  with  respect 
to  A ,  as  follows : 

Q  0.0004Q 

A.    —   • ,        ~   —    — — ~ 

2460  \/w.g.         \/w.g. 

Example. — Calculate  the  size  of  opening  in  each  of  the  regulators  in 
Splits  A,  B  and  Z),  in  the  illustration  previously  given  where  the  required 
circulation  was  as  follows: 

Required  circulation  Natural  pressure 

Split  A,  20,000  cu.  ft.;  2.17  Ib.  per  sq.  ft.  Regulator 

Split  B,  40,000  cu.  ft.;  11.55  Ib.  per  sq.  ft.  Regulator 

Split  C,  30,000  cu.  ft.;  13.89  Ib.  per  sq.  ft.  Free  split 

Split  D,  10,000  cu.  ft.;  2.98  Ib.  per  sq.  ft.  Regulator 

Solution.— The  first  step  is  to  find  the  pressure  due  to  the  regulator 
and  reduce  that  to  water  gage,  in  each  case.  The  pressure  due  to  the 
regulator  is  found  by  subtracting  the  natural  pressure  for  the  given 
split  from  that  of  the  free  split,  which  is  always  the  one  having  the 
greatest  natural  pressure.  Thus, 

Pressure  due  to  regulator  Water  gage 

Split  A,  13.89  -  2.17  =  11.72  Ib.  per  sq.  ft.;  11.72  -*•  5.2  =  2.25  in. 
Split  B,  13.89  -  11.55  =  2.34  Ib.  per  sq.  ft.;  2.34  -=-  5.2  =  0.45  in. 
Split  D,  13.89  -  2.98  =  10.91  Ib.  per  sq.  ft.;  10.91  4-  5.2  =  2.10  in. 

Substituting  these  values  for  the  water  gage  due  to  regulator  in  the 
formula  for  finding  the  area  of  opening, 


Split  A, 
Split  B, 
Split  D, 

0.0004Q 

0.0004  X  20,000 

5.33  sq.  ft. 
23.85  sq.  ft. 
2.7G  sq.ft. 

Ai  = 
Ad  = 

0.0004  X  40,000 

\/<X45 
0.0004  X  10,000 

V2710 

THEORY  OF  VENTILATION  235 

Use  of  the  Door  Regulator. — In  the  use  of  the  door  regu- 
lator, the  same  general  formulas  apply,  except  that  in  esti- 
mating the  quantity  of  air  that  will  pass  the  regulator,  for 
a  given  gage  or  pressure;  or  the  area  of  opening  necessary 
to  pass  a  given  quantity  under  such  gage,  no  allowance 
should  be  made  for  vena  contracta, which  gives  the  following: 

Quantity  of  air  passing  through  an  area  of  opening  A,  in  a 
door  regulator  under  a  water  gage  w.g., 


«  = 

Area  of  opening  required  to  pass  a  quantity  of  air  Q,  in  a 
door  regulator,  under  a  water  gage  w.g., 

0.00025^ 
Area,  A.  =       —7= 

Vw.g. 

Example. — What  must  be  the  width  of  opening  of  a  regulator  door 
where  the  height  of  the  entry  is  5  ft.  in  the  clear,  in  order  to  pass  40,000 
cu.  ft.  per  min.,  if  the  natural  pressure  for  the  required  circulation  pro- 
duces a  water  gage  of  1.25  in.  for  this  split  and  1.75  in.  for  the  free  split? 

Solution. — The  difference  of  pressure,  in  this  case,  is  equivalent  to  a 
water  gage  of  1.75  —  1.25  =  0.50  in.;  hence, 

0.00025  X  40,000 

A  =—       — ; -  =  14.14  sq.ft. 

V0.50 

Width  of  opening,  14.14  -r-  5  =  2.83  ft.,  or  2ft.  10  in. 

SECONDARY  SPLITTING 

Secondary  splitting  involves  the  principles  of  both  tan- 
dem and  split  circulations.  The  tandem  portion  consists  of 
one  airway  of  the  primary  split  and  the  two  airways  branch- 
ing from  this  and  forming  the  secondary  split  section. 

It  is  necessary  to  first  find  the  general  pressure  potential 
for  the  secondary  split  section.  This  is  equal  to  the  sum  of 
the  pressure  potentials  of  the  airways  forming  that  section. 
This  general  potential  for  the  secondary  split  is  then  com- 
bined with  the  corresponding  primary  potential,  according 
to  the  method  employed  for  a  tandem  circulation,  which  is 
then  regarded  as  one  branch  of  the  primary  split. 


236  MINE  GASES  AND  VENTILATION 

The  diagram  Fig.  33  shows  clearly  the  method  of  naming 
the  splits  and  indicating  them  by  symbols.  The  primary 
splits,  branching  from  the  point  where  the  air  current  is  first 
divided,  are  designated  by  the  letters  A,  B,  C,  etc.,  and  the 
corresponding  potentials  by  Xa,  Xb,  Xc,  etc. 

Secondary  splits  are  designated  AI,  A2)  etc.,  and  BI,  B%, 
etc.,  depending  on  the  primary  split  from  which  they  branch; 
and  the  corresponding  split  potentials  by  Xai,  Xa2,  Xbi,  Xbt, 
etc.  The  general  potential  for  a  primary  split  is  designated 
XQ,  and  for  a  secondary  split  Xao,  Xb<>,  etc. 

In  secondary  splitting  the  operation  is  much  simplified  by 
calculating  the  general  potential  for  each  consecutive  point 
or  section,  beginning  always  at  the  inby  end  of  the  system 
and  finding  first  the  general  potential  for  the  secondary  split; 


Return 


SPLIT   C>    5000  FT. 


FIG.  33. 

then  combining  this  in  tandem  with  the  corresponding  pri- 
mary potential;  and  using  this  result  to  find  the  general  po- 
tential for  the  primary  split,  in  the  same  manner  as  for  the 
secondary  split.  Two  formulas  only  are  necessary;  the  one 
expressing  the  summation  of  the  potential  values  for  a  split 
circulation,  and  the  other  a  similar  summation  for  a  tandem 
circulation.  They  as  as  follows: 
General  split  potential, 
General  tandem  potential  (see  p.  216), 

In  all  splitting  calculations  it  will  generally  be  found  more 
convenient  to  use  the  pressure  potential,  for  the  reason  that 
the  calculation  of  the  distribution  of  the  air  is  based  on  equal 
pressures,  for  all  splits  starting  from  one  point. 

Illustration. — Primary  splits  are  best  indicated  by  the 
large  letters,  as  Splits  A}  B}  C,  etc.  Secondary  splits  are 


THEORY  OF  VENTILATION  237 

named  after  the  primaries  in  which  they  occur;  thus  AI,  A2, 
etc.,  or  Bi,  Bz,  etc. 

The  corresponding  split  potentials  are  indicated  thus: 

i 

Primary  potentials,  Xa,  Xb,  Xc,  etc. 

Secondary  potentials,  Xa\,  Xaz;  Xbi  XL?;  Xc\  Xci;  etc. 

General  split  potentials,  Xao,  Xio,  Xco 

General  mine  potentials,  X0 

To  illustrate  the  calculation  of  the  effect  of  making  a  sec- 
ondary split  in  the  circulation  calculated  under  "  Unequal 
Splits"  (p.  224),  assume  the  air  is  again  split  in  C,  at  a  point 
500  ft.  inby  from  the  main  or  primary  split. 

Splits  A  and  B  are  the  same  as  before,  while  Split  C  is  now 
500  ft.  long;  Split  C},  1200  ft.  long;  and  Split  C8,  800  ft.  long. 
The  part  potential  values  for  the  splits  are,  then, 


Split  A,          Xp  =  eu/p  Xa       (as  before)          =  1.837 

Split  5,  Xb       (as  before)          =  1.623 

Split  C,  'x.-  48^1-^  =  2.629 

"48      "=1.697 


Split  Ci,  Xei  =  48  J 

Split  C2,  XcZ  =  48  J, 


1200  X  32 


=  2.078 


800   X   32 
General  split  potential,  SXC  =  1.697  +  2.078  =  3.775 

Combining  this  general  potential  for  Splits  Ci  and  C2  with 
the  potential  for  Split  C,  in  tandem,  we  have, 


Part  potential  factors, 


(Tandem  circulation)          X2C       2.6292 

=  °-0702 


Tandem  value,         Xf0  =  S  (l/X2c)  .....       0.2149 

General  part  potential, 

(Primary  split  C)  Xco  =  ^A^  =  2.157 

Part  potential,  Split  A,     Xa  =  1.837 

Part  potential,  Split  B,     Xb  =  1.623 

Mine  pressure  potential,   Xpo  .....       5.617 


238  MINE  GASES  AND  VENTILATION 

Mine  power  potential,  (After  splitting) 


=  3.160 

Mine  power  potential,  (Before  splitting,  p.  225) 

Xul  =  \/4i6362  =  2.780 


For  a  constant  power,  the  quantity  ratio  is  equal  to  the 
power-potential  ratio;  thus, 

Q*  =  X*_2.  ( 
~' 


Xul'          75,000       2.78' 

n        75,000  X  3.16       Qr 

62  =  -    -2~78~"        =  85,240  CM.  //.  pe 

Mine  pressure,    p  =  k($-}  *  =  0.00000002/|5^)  2  =  4.6  Ib. 
VA^7  V5.617/  per  sq.ft. 

Power  on  the  air,  u  =  k  (—-}  *  =  0.00000002  (^  |?)  *  =  1  1  . 
\  A  u/  \  o.lb  / 

The  natural  division  of  the  main  air  current  of  85,240  cu.  ft. 
between  the  three  primary  splits,  A,  B,  C;  and  the  two  second- 
ary splits  Ci,  C2,  in  the  last  example,  is  calculated  first  for 
the  primary  division,  and  then  for  the  secondary,  as  follows: 
Primary  splits, 

Part  pressure  Natural          Required 

potentials  (cu.  ft.  per  min.) 


Xa  =  1.837;  qa  =  X  85,240  =  27,880      20,240 

O. 


Xb  =  1.623;  qb  =  X  85,240  =  24,630      16,000 


Xco  =  2.157;  qc  =  l~~  X  85,240  =  32,730      40,000 
o  . 


2XP  =  5.617      Q=  ......  85,240      85,240 

Secondary  splits, 

Xel  =  1.697;  qel  =  \^  X  32,730  =  14.710       25,000 

o  .  /  «O 


XcZ  =  2.078;  qc2  =  =  X  32,730  =  18.020        15,000 

o  .  775 

SXP  =  3  .  775  32,730      40,000 


THEORY  OF  VENTILATION  239 

The  natural  pressures  are  then  calculated  for  the  required 
circulation  of  air  in  each  split.  The  highest  pressure  of  the 
secondary  splits  determines  the  secondary  pressure,  which 
must  be  added  to  the  natural  pressure  of  the  tandem  airway, 
to  obtain  the  effective  primary  pressure  for  Split  C.  Finally, 
the  highest  primary  pressure  determines  the  primary  pressure, 
which  is  the  pressure  for  the  entire  split  circulation.  The 
process  is  as  follows: 

Secondary  pressures, 

<••-*(£)'; 

/OC   f}(\0\  2 

Pd  =  0.00000002  (p^)    =4.341  Ib.  per  sq.  ft. 

pc.  =  0.00000002  (^-^g)  2  =  1  -042  Ib.  per  sq.  ft. 

Tandem          pc  =  0.00000002        '         '  =  4  .  630  Ib.  per  sq.  ft. 


Primary  pressures,  pc0  =  2pc      8.971/6.  per  sq.ft. 

/2Q  240\  2 
pa  =  0.00000002  (y^)    =5.067  Ib.  per  sq.  ft. 

pb  =  0.00000002  (\-jJ23)  2  =  1-944  Ib.  per  sq.  ft. 

Qv 
Horsepower,  H  =  ^-^  ; 

„       85,240  X  8.971 

--     =23-17/J- 


The  secondary  pressure,  as  determined  by  the  highest  nat- 
ural pressure  in  those  splits,  is  that  in  Split  Ci,  which  is  4.341 
Ib.  per  sq.  ft.  Likewise  the  primary  pressure  (the  highest  of 
those  splits)  is  that  of  the  tandem  split  Co,  which  is  8.971  Ib. 
per  sq.  ft.  These  pressures  are  indicated  above  by  the  heavy 
type. 

Regulators.  —  The  difference  between  the  secondary  pressure 
and  the  natural  pressure  in  any  secondary  split  is  the  pres- 
sure due  to  the  regulator  or  the  regulator  pressure  for  that 
split.  The  same  is  true  for  primary  splits. 


240  MINE  GASES  AND  VENTILATION 

The  pressures  due  to  the  regulators  required  in  Splits  A, 
B  and  C2,  in  order  to  accomplish  the  required  distribution  of 
air  are,  therefore,  as  follows: 

Split  A,  8.971  -  5.067  =  3.904  Ib.  per  sq.  ft.  (0.751  in.  w.g.) 
Split  B,  8.971  -  1.944  =  7.027  Ib.  per  sq.  ft.  (1.351  in.  w.g.) 
Split  C2,  4.341  -  1.042  =  3.299  Ib.  per  sq.  ft.  (0.634  in.  w.g.) 

The  necessary  area  of  opening  in  a  regulator  to  pass  the 
required  quantity  of  air,  under  the  given  water  gage  is  calcu- 
lated as  follows: 

„  0.0004? 

Box  regulator,     A  =  — =  ~ ; 
Vw.g. 

0.0004X  29,240       1Q  _         . 
Aa  =—     —7=  -  =  13.5  sq.  ft. 

\/0.751 

0.0004  X  16,000       _  _•        . 

Ab  =  -          , -  =  5.5  sq.ft. 

Vl.351 

0.0004  X  15,000       _  r        ,, 
Ac2  =  -       —7=  -  =  7.5  sq.ft. 

V0.634 

If  door  regulators  are  used  the  openings  have  the  following 
areas : 

0.00025? 

Door  regulator,  A  = j — — ; 

Vw.g. 

0.00025  X  29,240  ft 

Aa  =  -  .      — - —  =  8Asq.fi. 

V0.751 

0.00025  X  16,000 


VI. 351 


=  .3  A  sq.ft. 


0.00025  X  15,000        .  _       A 

Ac2  =  -        —j=—    -  =  4.7  sq.ft. 
V0.634 

The  results  of  making  the  secondary  split  in  Primary  C 
may  therefore  be  summarized  as  follows: 

The  above  comparison  shows:  (1)  The  increase  in  the 
quantity  of  air  in  circulation  and  the  decrease  in  the  unit 
pressure  and  water  gage,  for  the  same  power  on  the  air, 
caused  by  making  a  small  secondary  split,  in  one  of  the 
original  primaries.  (2)  The  large  increase  of  power  on  the 


THEORY  OF  VENTILATION 


241 


air  and  pressure  and  water  gage  necessary  to  make  the  re- 
quired distribution  of  air,  in  this  case. 


Distribution  of  air 


Natural  circulation 
(No  regulators) 

Required 

(Regulators) 

Split  A  (cu.  ft.  per  m.)  

29,720 
26,260 
19,020 

27,880 
24,630 

(32,730) 
14,710 
18,020 

29,240 
16,000 
(40,000) 
25,000 
15,000 

Split  B                 

Split  C 

Split  d  

Split  C2              

Totals  

75,000 
5.2 
1.0 
11.9 

85,240 
4.6 
0.88 
11.9 

85,240 
8.97  ' 
1.72 
23.17 

Pressure  (Ih.  per  sq.  ft.)  
Water  gage  (in  ) 

Horsepower  on  air  (hp.)  

Example. — An  air  current  of  120,000  cu.  ft.  per  min.  is  passing  in  a 
mine  in  two  splits,  as  follows: 

Split  A,          5  X  10  ft.,  20,000  ft.  long;  40,000  cu.  ft.  per  min. 
Split  B,          5  X  10  ft.,    5,000  ft.  long;  80,000  cu.  ft.  per  min. 

More  air  being  required,  a  careful  investigation  shows  that  Split  A 
can  be  again  divided  at  a  point  2000  ft.  inby  from  the  foot  of  the  down- 
cast shaft,  thereby  forming  two  secondary  air  splits,  each  5  X  10  ft., 
8000  ft.  long,  including  the  return.  This  would  make  Split  A  4000  ft. 
long  including  the  return.  With  the  same  power  on  the  air,  what 
quantity  of  air  will  be  circulated  in  this  mine  after  dividing  Split  A  ? 

Solution. — The  first  step  is  to  calculate  the  potential  values  of  the 
different  sections  or  splits,  both  before  and  after  dividing  Split  A  to  form 
the  two  secondary  Splits-  A i  and  Az.  This  being  a  comparison  of  two 
circulations,  it  is  possible  to  use  the  relative  potentials,  reducing  the 
areas,  perimeters  and  lengths  to  their  lowest  relative  values,  which 
gives  the  following: 

Before  dividing  Split  A : 


Split  A, 
Split  B, 


=  50;  o  =  30;  I  =  20,000 
=  50;  o  =  30;  I  =    5,000 


(Relative  values) 


After  dividing  Split  A : 

Split  A,  a  =  50;  o  =  30;  I  =  4,000 

Split  J5,  a  =  50;  o  =  30;  I  =  5,000 

Split  Ai,  a  =  50;  o  =  30;  I  =  8,000 

Split  A 2,  a  =  50;  o  =  30;  I  =  8,000 

16 


a  =  1 

0    =    1 

I  =  20 

a  =  1 

0    =    1 

I  =    5 

a  =  1 

0    =    1 

I  =    4 

a  =  1 

0    =    1 

I  =    5 

a  =  1 

0    =    1 

I  =    8 

a  =  1 

a  =  1 

I  =    8 

242  MINE  GASES  AND  VENTILATION 

Relative  potentials,  before  division : 

T  =  —7=  =  0.2236 
^  1        A/20 

-  0.6708 

5X1  h  =  °'4472  ' 

o  X  1         A/5 

Relative  potentials,  after  division: 
X.  =  «Ji  =  1 


Xi,  =  Same  as  before  =  0.4472 

T~        i 


U'8_ 

Wslh  '  T7«  '  °-3838 


=  0.707 


Tandem  summation  (Xa  and  A'0o) : 


=  =  0.4082 


+  1/A200       Vl/0.52  +  1/6.707* 
A  2  =  A,  +  Xb  =  0.4082  +  0.4472  =  0.8554 

Since  the  power  is  the  same,  before  and  after  division  and  calling  these 
respective  general  potentials  Xit  A2,  we  have 

jOil   =  Q*.  f     ,  120,0003  =  _Q,»_ 
(Xi)2      A22'  0.67082        0.8554* 

Q2  =  120,000^  (^|^)2    -  141,100  en.  ft.  per  min. 


THEORETICAL  CONSIDERATIONS  IN  SPLITTING 

Theory  assumes  that  when  an  air  current  traveling  in  an 
airway  divides,  at  a  certain  point  called  the  "point  of  split," 
into  two  separate  currents  or  "splits,"  the  unit  pressure  (p) 
at  the  point  of  split  is  common  to  each  split.  In  other  words, 
two  splits  starting  from  the  same  point  in  a  mine  have  the 
same  unit  pressure  (p)  and,  for  the  same  sectional  area  (a), 
the  resistance  (R  =  pa)  is  the  same  for  each  split.  The  same 
holds  true  for  any  number  of  splits  (ri)  of  equal  area. 

Whether  the  unit  pressure  (p)  or  the  unit  work  (pv)  is  the 
factor  common  to  each  of  two  or  more  splits  starting  from  the 
same  point  will  not  be  discussed  here.  The  law  of  dynamic 


THEORY  OF   VENTILATION  243 

equilibrium  of  fluids  points  to  the  equality  of  unit  work  for 
each  split.  The  comparison  of  the  relation  of  the  quantity  of 
air  (q),  the  rubbing  surface  (s)  and  the  sectional  area  (a), 
on  these  two  bases  of  reasoning,  is  as  follows: 

Unit  pressure  Unit  work 

ksq2  u       ksq* 

a3  a         a4 

For  constant  unit  pressure :  For  constant  unit  work : 


q  vanes  as  a  •%/-  q  varies  as 

\s 

Practical  Conditions. — In  considering  the  practical  results 
of  splitting  the  air  current  in  a  mine,  it  may  be  assumed  that 
the  power  on  the  air  ([/)  at  the  mouth  (intake)  of  the  mine 
remains  constant.  Assuming  a  number  of  splits  (n),  starting 
from  the  same  point  in  the  mine,  at  or  near  the  shaft  bottom 
or  mine  entrance,  the  total  area  of  passage  is  na  and  the  for- 
mula for  power  is  then 


_. 

"  (na)3 

which  shows  that,  since  in  any  case  U,  k,  s  and  a  are  each 
constant,  Q3  varies  as  n3,  or  Q  varies  as  n,  which  is  the  num- 
ber of  equal  splits,  each  having  an  area  a. 

In  other  words,  the  quantity  of  air  circulated  in  a  given 
mine,  by  a  given  power  on  the  air  (effective  power),  is  pro- 
portional to  the  number  of  splits,  assuming  the  splits  all  start 
from  the  mine  entrance  or  so  near  to  it  that  the  resistance  of 
the  main  intake  entry,  slope  or  shaft  may  be  ignored.  Under 
these  conditions,  splitting  the  air  has  no  effect  to  alter  the 
velocity  or  the  resistance  in  the  mine. 

When  the  point  of  split,  however,  is  some  distance  inby 
from  the  mouth  of  the  mine  or  " daylight"  the  effect  of  split- 
ting the  air,  in  that  case,  is  to  cause  a  disproportion.  The 
quantity  of  air  circulated  by  a.  given  power  no  longer  varies 
as  the  number  of  splits;  but  the  ratio  of  increase  in  volume 
is  less,  because  the  power  on  the  air  at  the  mouth  of  the  splits 
is  decreased  by  splitting. 


244  MINE  GASES  AND  VENTILATION 

Assuming,  as  before,  a  constant  power  on  the  air  at  the 
mouth  of  the  mine,  since  the  quantity  has  been  increased  by 
splitting,  both  the  velocity  and  resistance  have  been  increased 
in  the  main  airway,  which  absorbs  more  power  thus  decreas- 
ing the  power  on  the  splits. 

Effect  of  Splitting  on  Velocity.  —  In  order  to  show  the  gen- 
eral effect  of  splitting  the  air  current,  at  any  point  in  a  mine, 
on  the  velocity  (VG)  in  the  shaft  or  main  airway  and  the  velocity 
(vi)  in  the  splits,  it  is  necessary  to  know  the  ratio  (m)  of  the 
rubbing  surface  (si)  in  the  splits,  to  that  of  (s0)  in  the  shaft 
or  main  airway;  also,  the  ratio  (n)  of  the  total  area  (Ai)  of 
the  splits,  to  that  of  (Ao)  in  the  shaft  or  main  airway. 

Then,  si  =  raso;     andAi  =  nA0;  (1) 

and,  since  for  a  given  quantity  the  velocity  varies  inversely 
as  the  area, 

*-*  ,        ~        ,2) 

But,  the  power  on  the  air  (u)  at  the  mouth  of  the  mine  is 
equal  to  the  power  (MO)  absorbed  in  the  shaft  or  main  airway, 
or  both,  plus  the  power  (MI)  absorbed  in  the  splits. 

M  =  MO  +  MI  (3) 

or,  expressed  in  terms  of  the  mine,  since  M  =  ksv3, 

u  =  k(s0v03  +  s^i3)  (4) 


Substituting  for  Si  and  Vi3  the  values  given  in  Equations  1 
and  2,  gives  after  simplifying 


o    „  0 

u  =  fcWl  +  -3     =  fcW—r-  (5) 

Equation  5  shows  clearly  that,  for  a  constant  power  on  the 
air  at  the  mouth  of  a  mine,  in  splitting, 

T? 

#o  varies  as    3  (6) 

V  n3  +  m 

and,  observing  Equation  2, 

vi  varies  as    3/  __  —  =:  (  7) 

\/n3  +  m 


THEORY  OF   VENTILATION  245 

It  appears  from  the  last  two  equations  that  as  the  ratio 
of  the  split  area  to  the  shaft  or  main-intake  area,  represented 
by  n,  is  increased  the  main-intake  velocity  (VQ)  is  increased, 
while  the  split  velocity  (vi)  is  decreased,  the  increase  and  de- 
crease of  velocity,  however,  being  less  rapid  than  the  change 
in  the  area  ratio. 

Effect  of  Splitting  on  Quantity. — The  quantity  of  air  in 
circulation  varies  directly  as  the  intake  velocity  v0;  or,  for  a 
constant  power  (u)  on  the  air, 

Q  varies  as  3/—=  (8) 

V  ft3  +  ra 

Effect  of  Splitting  on  the  Mine  Resistance. — The  total  mine 
resistance  is  the  sum  of  the  main-intake  and  split  resistances. 

Thus,  R  =  /c(W    +  sit  i2)  (9) 

and  R 

Finally,  from  Equations  6  and  10  is  derived 

n2  +  m,  /11X 

R  varies  as    3/  =  (11) 


PRACTICAL  PROBLEM 

Example. — A  current  of  25,000  cu.  ft.  per  min.  is  passing  in  a  shaft 
mine.  The  shafts  are  8  X  12  ft.  in  section  and  250  ft.  deep.  The  air- 
ways are  6  X  10  ft.  and  15,000  ft.  long,  including  the  return,  (a)  What 
is  the  water  gage  due  to  this  circulation?  (6)  Assuming  the  power 
applied  to  the  fan  shaft  remains  unchanged  and  the  current  is  divided 
into  two  equal  splits,  at  a  point  1500  ft.  inby  from  the  foot  of  the  shaft, 
what  volume  of  air  may  be  expected  to  be  passing?  (c)  What  will  be 
the  water-gage  reading  on  the  fan  drift  and  at  the  bottom  of  the  shaft, 
after  splitting? 

Solution. — The  rubbing  surface  and  sectional  area  of  the  shafts  and 
airways  are,  respectively,  as  follows: 

Shafts —  Sq.  Ft. 

Rubbing  surface 2(8  +  12)2  X  250  =    20,000 

Sectional  area 8  X  12  =           96 

Airways  (total) — 

Rubbing  surface 2(6  +  10)15,000  =  480,000 

Sectional  area..                                                             .   6  X  10  =           60 


246  MINE  GASES  AND  VENTILATION 

Main  airway — 

Rubbing  surface 2(6  +  10)2  X  1500  =    96,000 

Sectional  area 6X10=  60 

Two  equal  splits — 

Rubbing  surface 2(6  +  10)12,000  =  384,000 

Sectional  area 2(6  X  10)  =          120 

The  relative  part  potential  factors  are  then : 

Before  splitting — 

Shaft,  .  ..(±.  or    1  \   -  A  -  ^°™      =  0.0226 


Airwas  (total)  ...............................   =  =  2.2223 


General  relative  mine  potential  factor  (  S  -==-5!   ................  2  . 


2449 

After  splitting  — 

Shafts  (as  before)  ............  '.  ..........................   0.  0226 

1          s        96,000 
6Q3 


, 
Main  airway  .........................  -        =  —  =          3      =  0.4444 


spats 


General  relative  mine  potential  factor  (  S  p-^1    ................  0.6892 

(a)  Water  gage  (before  splitting)  — 

1  \         0.00000002  X  25,0002  X  2.2449 


(6)  For  a  constant  power  on  the  air,  the  quantity  varies  directly  as 
the  mine  power  potential;  but,  for  a  constant  power  applied  to  the  fan 
shaft,  owing  to  the  efficiency  of  the  fan  varying  inversely  as  the  3/5 
power  of  the  potential  Xu  the  quantity  varies  as  the  4/5  power  of  that 
potential. 

The  mine  potentials,  in  this  case,  are, 

Before  splitting— Since  l/X3«i  =  2.2449;  Xui  =    .    1  =  0.7637 


After  splitting— Since  1/X3«2  =  0.6892;  Xut  =    .x  =  1.1321 

^0.6892 

Then,  for  a  constant  power  applied  to  the  fan  shaft,  the  quantity  of 
air  in  circulation  varies  as  the  4/5  power  of  the  power  potential,  which 
gives  for  the  circulation  after  splitting 


*  =  25,000  =  34,250  cu.  ft.  per  min. 


(c)  Water  gage  (after  splitting).  —  In  the  fan  drift  the  gage  is 

0.00000002  X  34,2502  X  0.6892 
w.g,  =  --  —  —  -  =  3.1  in. 


THEORY  OF   VENTILATION  247 

To  find  the  gage  at  tho  shaft  bottom  it  is  necessary  to  deduct  the 
potential  factor  for  the  two%shafts  from  the  total  potential  factor  for  the 
mine  after  splitting;  thus 

J-  -  _L  =  0.6892  -  0.0226  =  0.6666 

Ap*         \pol 

Then,  since  the  gage  is  proportional  to  this  potential  factor,  the  gage  at 
the  bottom  of  the  shaft  is 

.  0.6666 
'"•"•=3-1X  06892 

Relative  Variation  of  Factors.  —  The  following  relation  of  some  of  the 
more  important  factors  in  the  ventilation  of  mines  by  means  of  centrifugal 
fans  is  based  on  the  results  of  many  experiments: 

Power  on  Air  Constant  (KU  =  u)  — 

Unit  pressure,  p  varies  inversely  as  Q 

1       J/~s 


p  varies  as 

Xu 

Quantity,  Q  varies  as  X 

Power  Applied  to  Fan  Shaft  Constant  (U)— 

Efficiency,  1/K*  varies  as  Xu3  =  Xp2  =  az 

Effective  power,  u  varies  as  K 

Quantity,  Q&  varies  as  AV 

Mine  Potential  Constant  (Xu3  =  Xp2  =  a3/s)  — 

Effective  power,  u  varies  as  Q3 

Quantity,  Q6  varies  as  n4 

Water  eage,  (w.g.)&  varies  as  n8 


SECTION  VII 
PRACTICAL  VENTILATION 

CONDUCTING  AIR  CURRENTS,  AIR  BRIDGES — GENERAL  PLAN 
OF  MINE — DISTRIBUTION  OF  AIR  IN  THE  MINE — SPLIT- 
TING AIR  CURRENTS — SYSTEMS  OF  VENTILATION — SYSTEMS 
OF  MINE  AIRWAYS. 

The  first  step,  in  the  practical  ventilation  of  a  mine,  is 
to  determine  the  volume  of  air  that  will  be  required  in  order 
to  maintain  a  pure  and  wholesome  atmosphere  in  the  mine 
workings.  This  will  depend  on  conditions,  such  as  the  size 
and  depth  of  the  mine;  thickness  and  inclination  of  the 
seam;  character  and  quality  of  the  coal;  kind  and  quantity 
of  gas  generated;  methods  of  working  the  seam  and  mining 
the  coal.  Aside  from  these  conditions  the  volume  of  air 
must  always  be  sufficient  to  meet  the  requirements  of  the 
mine  law. 

The  second  question  to  be  determined  is  the  general  ventila- 
ting pressure  or  water  gage,  under  which  the  mine  is  to  be 
ventilated.  This  will  depend  on  the  possible  extent  and 
size  of  the  workings  and  the  power  available.  The  water 
gage,  in  mining  practice,  varies  from  a  fraction  of  an  inch  to  3 
or  4  in.,  in  this  country;  and  higher  gages  are  in  use  in  the 
deep  mines  of  Belgium  and  other  countries.  The  best  practice, 
however,  employs  such  a  system  of  mining  that  the  required 
volume  of  air  can  be  circulated  under,  say  1  or  2  in.  of  water 
gage.  This  can  only  be  accomplished  by  so  planning  the  mine, 
in  the  start,  that  it  can  be  divided  into  separate  ventilation 
districts.  The  number  of  ventilation  districts  should  increase 
with  the  development  of  the  mine.  Each  district  is  thus 
ventilated  by  a  separate  air  split  or  current,  which  insures 
good  air,  besides  reducing  the  water  gage  necessary  for  the 
ventilation  of  the  mine. 

248 


PRACTICAL  VENTILATION  249 

Power  Required  to  Produce  a  Given  Circulation. — having 
decided  on  the  volume  of  air  required  and  the  water  gage, 
these  factors  determine  the  power  that  will  be  necessary  to 
produce  the  circulation.  The  power  on  the  air  may,  gen- 
erally, be  safely  taken  as  60  per  cent,  of  the  indicated  horse- 
power of  the  engine  driving  the  ventilating  fan.  For 
example,  the  circulation  of  75,000  cu.  ft.  of  air  against  a  water 
gage  of  2  in.  will  require,  with  a  safe  margin,  an  engine 
capable  of  developing 

75,000  X  2  X  5.2 


0.60  X  33,000 


=  39.4,  say  40  hp. 


The  above  calculation  assumes  a  properly  designed  ven- 
tilating fan,  since  a  poorly  designed  fan,  or  a  fan  working 
under  conditions  for  which  it  is  not  adapted,  may  give  an 
efficiency  of  only  40  or  50  per  cent.;  or  at  times  this  may  not 
exceed  25  per  cent.,  under  particularly  adverse  conditions. 
An  unsuspected  negative  air  column  existing  in  some  portion 
of  the  mine  may  be  the  hidden  cause  of  the  low  efficiency 
of  a  ventilating  fan. 

CONDUCTING  AIR  CURRENTS 

Conducting  Air  Currents  in  Mines. — To  conduct  the  air  on 
its  course  through  the  mine,  doors,  stoppings,  brattices,  air- 
crossings,  or  bridges — either  overcasts  or  undercasts — are 
employed  to  deflect  the  air  current.  When  the  air  is  divided 
and  made  to  travel  in  two  or  more  splits  regulators  are  used  to 
proportion  the  quantity  of  air  to  the  requirements  in  each 
split. 

In  Fig.  34  are  shown  two  forms  of  self-closing  doors  used  in 
mines.  There  are  many  different  methods  in  use  to  prevent 
a  mine  door  standing  open,  but  these  are  as  practical  as  any. 
The  door  on  the  left  is  shown  with  canvas  flaps  to  stop  the 
leakage  of  air.  Both  doors  swing  either  way,  being  heavy 
enough  to  overcome  .  the  pressure  of  the  ventilating  current. 

Stoppings,  in  mine  ventilation,  are  built  in  entries  or  in 
crosscuts  for  the  purpose  of  closing  the  passage.  When  built 


250 


MINE  GASES  AND   VENTILATION 


in  crosscuts  they  serve  to  carry  the  air  current  forward  to  the 
head  of  the  entry.  A  common  form  of  stopping  consists  of 
two  walls  of  slate  or  rock  built  10  or  12  in.  apart  and  the  space 
between  them  filled  tight  with  road  dirt  or  sand.  More  sub- 
stantial stoppings  are  built  of  brick  laid  in  cement,  or  of 
concrete. 

In  Fig.  34  is  also  shown  the  right  and  the  wrong  way  of 
erecting  a  line  of  brattice  in  a  pair  of  headings.     As  shown  in 


FIG.  34. 

each  of  the  figures,  a  row  of  posts  is  set,  one  at  a  time,  and 
canvas  or  brattice  boards  nailed  to  them  on  the  intake  side. 
The  posts  are  stood  18  in.  or  2  ft.  from  the  right  rib  if  the 
intake  is  on  the  right,  or  the  left  rib  if  on  the  left.  The 
same  order  is  followed  on  the  return  airway  or  heading.  The 
work  of  nailing  the  canvas  or  boards  to  the  post  is  done  on 
the  fresh-air  side  and  the  brattice  extended  as  the  current 
sweeps  away  the  gas  accumulated  in  these  headings.  The 


PRACTICAL  VENTILATION  251 

arrows  show  the  course  of  the  air  as  it  circulates  around  the 
brattice  in  each  heading. 

Air  Bridges. — In  Fig.  34  are  also  shown  different  methods  of 
constructing  air  bridges  in  mines,  for  the  purpose  of  conducting 
one  air  current  across  another.  First  is  shown  a  standard 
type  of  overcast  built  of  reinforced  concrete.  Immediately 
below  this  is  shown  two  common  types  of  air  bridges,  an  over- 
cast and  an  undercast.  In  the  "undercast"  shown  on  the 
right,  the  cross-current  of  air  is  conducted  under  the  main  road 
or  heading,  the  bridge  in  that  case  forming  the  floor  of  the 
roadway.  A  safer  and  more  serviceable  form  of  air  bridge, 
however,  is  the  "overcast"  shown  on  the  left,  by  which  the 
cross-current  is  carried  over  the  haulage  road.  The  under- 
cast  possesses  the  disadvantage  that  it  cannot  be  drained  and 
may  become  flooded  and  cut  off  the  air  current  completely. 

Natural  Overcast. — Owing  to  the  difficulty  of  keeping  air 
bridges  air-tight,  and  for  the  further  reason  that  the  possible 
destruction  of  an  air  bridge  by  an  explosion  would  cut  off 
the  circulation  of  air  in  the  district  fed  by  that  means,  a 
natural  overcast  is  frequently  referred. 

In  the  lower  right-hand  corner  of  Fig.  34  is  shown  a  natural 
overcast  as  driven  in  the  upper  portion  of  a  thick  coal  seam, 
although  the  same  form  of  overcast  is  often  driven  in  the  rock 
strata  overlying  a  thinner  seam.  Such  a  natural  overcast 
is  formed  by  starting  an  uprise  in  the  roof  of  the  cross-entry, 
a  short  distance  on  either  side  of  the  main  heading,  and  then 
driving  a  crosscut  in  the  solid  formation  above  and  across  the 
main  roadway,  thereby  forming  a  wholly  separate  air  passage 
for  the  intake  and  return  air  currents. 

Regulators. — As  described  previously  and  illustrated  in  Fig. 
32,  regulators  are  used  to  divide  an  air  current  in  any  desired 
proportion  between  two  entries  or  splits.  The  "box"  regu- 
lator is  commonly  placed  on  the  return  airway,  where  it  offers 
no  obstruction  to  haulage,  while  the  "door"  regulator  is  al- 
ways placed  on  the  intake.  The  use  and  effect  of  these  two 
forms  of  regulators  are  fully  treated  under  "Proportionate 
Division  of  Air,"  page  231,  in  the  section  "Theory  of 
Ventilation." 


252  MINE  GASES  AND  VENTILATION 

GENERAL  PLAN  OF  MINE 

Requirements. — In  the  planning  or  laying  cut  of  a  mine  the 
most  careful  consideration  must  be  given  to  the  questions  of 
ventilation,  drainage  and  haulage,  as  these  arrangements,  to 
a  great  degree,  determine  the  successful  operation  of  the 
mine. 

In  order  to  insure  the  safe  and  economic  extraction  of  the 
coal,  the  same  careful  consideration  must  be  given  to  ascer- 
taining the  extent  and  character  of  the  seam,  its  depth  below 
the  surface,  inclination  and  thickness,  the  character  of  the 
roof  and  floor  and  the  hardness  of  the  coal;  its  cleavages  and 
faults,  impurities,  etc. 

The  information  thus  gained  will  be  of  the  first  import- 
ance in  deciding  on  the  most  suitable  method  of  mining  to 
adopt,  in  order  to  secure  the  largest  returns  on  the  invest- 
ment, the  most  complete  extraction  of  the  coal  and  the  great- 
est safety  in  mining  the  same. 

Economy  and  Efficiency. — The  economic  ventilation  of  a 
mine  premises  the  circulation  of  the  required  air  volume, 
with  the  least  expenditure  of  power.  Efficient  ventilation  re- 
quires the  circulation  and  proportionate  distribution  in  the 
mine  workings,  of  such  a  volume  of  air  as  will  not  only  meet 
the  requirements  of  the  law,  but,  likewise,  produce  the  neces- 
sary velocity  in  all  roads  and  passageways  and  at  the  working 
faces  of  all  headings  and  chambers,  so  as  to  sweep  away  the 
smoke  and  gases  that  would  otherwise  accumulate  therein; 
and  to  so  ventilate  all  waste,  void  and  abandoned  places  as  to 
prevent  them  from  becoming  a  menace  to  the  safety  of  the 
mine  as  reservoirs  for  the  accumulation  of  gas. 

Drainage. — Economic  mine  drainage  requires  such  a  dis- 
position of  the  openings  driven  in  the  seam  for  the  extrac- 
tion of  the  coal,  including  all  passageways,  headings  and 
chambers,  that  the  water  coming  from  the  strata  will  flow 
by  gravity,  either  to  the  main  sump  at  the  shaft  or  slope 
bottom,  or  to  certain  gathering  centers  from  which  it  can 
be  readily  siphoned  to  the  main  sump  or  pumped  directly 
to  the  surface. 


PRACTICAL  VENTILATION  253 

In  practically  level  seams  or  seams  having  slight  inclina- 
tion, the  question  of  drainage  does  not  materially  affect 
the  general  mine  plan.  In  this  case,  good  roadside  ditches 
afford  the  necessary  waterways  by  which  the  underground 
water  flows  to  the  sumps  provided  to  receive  it  Such  sumps 
or  catch  basins  are  located  at  one  or  more  convenient  low 
places  or  " swamps,"  in  the  mine,  where  it  is  possible  to 
install  a  pump  of  sufficient  size  to  handle  the  water  of  that 
section  at  all  times. 

The  rooms  or  chambers,  in  practically  level  seams,  are 
turned  off  both  entries  of  a  pair,  which  greatly  reduces  the 
expense  of  entry  driving  and  necessary  maintenance  of  road- 
ways and  air-courses. 

In  inclined  seams  the  direction  and  amount  of  pitch  are 
controlling  factors  in  determining  the  general  plan  of  the 
mine,  in  respect  to  the  course  of  main  roads,  cross-headings 
and  rooms  or  chambers.  In  respect  to  drainage,  it  is  im- 
portant to  drive  all  such  openings  to  the  rise,  in  order  to 
avoid  the  annoyance  and  expense  of  providing  artificial 
means  of  draining  the  working  faces. 

Haulage. — Economic  mine  haulage  requires  that  the  coal, 
like  water  must  gravitate,  as  far  as  practicable,  from  the 
coal  face  where  it  is  mined,  to  the  foot  of  the  shaft  or  slope 
opening  from  whence  it  is  hoisted  to  the  surface. 

In  level  seams,  the  question  of  haulage  does  not  affect 
the  plan  of  mine;  but,  in  seams  of  more  or  less  inclination, 
it  becomes  a  matter  of  first  consideration. 

In  inclined  seams,  it  is  always  possible  to  drive  the  main 
haulage  roads  in  such  a  direction  that  the  grade  of  the  road 
will  not  only  favor  the  movement  of  the  loaded  cars, 
but  will  be  such  that  the  power  required  to  haul  the  loaded 
trip  out  of  the  mine  will  be  equal  to  that  necessary  for  hauling 
the  empty  trip  back  into  the  mine.  This- is  called  the  " eco- 
nomical grade." 

The  grade  of  any  road,  or  the  road  grade,  in  an  inclined 
searn,  may  be  calculated  when  the  angle  of  inclination  of 
the  seam  and  the  angle  the  road  makes  with  the  strike  of 
the  seam  are  known,  by  the  following  rule: 


254 


MINE  GASES  AND  VENTILATION 


Rule. — -The  tangent  of  the  grade  angle  is  equal  to  the 
tangent  of  the  angle  of  inclination  of  the  seam,  multiplied 
by  the  sine  of  the  angle  the  road  makes  with  the  strike  of 
the  seam. 

Or,  calling  the  angle  between  the  road  and  the  strike  of 
the  seam,  the  "road  angle,"  this  angle  is  calculated  by  the 
use  of  the  formula 


sin  road  angle  = 


tan  grade  angle 
tan  inclination 


There  is  shown  clearly  in  Fig.  35,  a  perspective  plan  of  a, 
pair  of  entries  with  rooms  turned  off  the  haulage  road.     The 


FIG.  35. 

left-hand  entry  is  the  return  air-course,  while  the  haulage 
road  is  the  intake.  •  A  canvas  or  curtain  hung  on  the  entry 
just  inside  of  the  mouth  of  the  first  room  deflects  the  intake 
air  mostly  into  the  rooms,  where  it  passes  through  the  break- 
throughs from  room  to  room.  Better  results  are  generally 
obtained  when  the  breakthroughs  are  staggered  Or  not  driven 
directly  opposite  each  other,  as  shown  in  the  figure.  The 


PRACTICAL   VENTILATION 


2.55 


FIG.  36. 


FIG.  37. 


256  MINE  GASES  AND  VENTILATION 

crosseuts  on  the  entries  are  closed  by  substantial  stoppings, 
except  the  last  crosscut  where  the  intake  air  passes  into  the 
return,  as  shown  by  the  arrows. 

General  Plan,  Level  Seam. — In  Fig.  36  is  illustrated  the 
general  plan  of  a  mine  shaft  bottom  in  a  level  seam.  At 
times,  it  may  be  necessary  to  drive  the  shaft  bottom  at  an 
angle  with  the  main  and  cross-entries,  as  shown  in  Fig.  37, 
in  order  to  square  the  hoisting  shaft  with  the  loading  tracks 


FIG.  38. 

on  the  surface.  In  each  of  these  figures  the  intake  current  is 
divided,  forming  two  main  splits  of  air  near  the  foot  of  the 
downcast  or  air  shaft  and  these  main  splits  are  again  divided 
two  or  more  times  to  ventilate  different  sections  of  the  mine, 
as  indicated  by  the  arrows. 

Ventilation  of  Longwall  Workings.— Figs.  38  and  39  are 
two  general  plans  of  longwall  workings,  showing  the  main 
air  current  carried,  in  two  or  more  splits,  from  the  bottom 


PRACTICAL  VENTILATION 


257 


of  the  downcast  shaft  directly  to  the  working  face,  where  it 
is  again  divided  and  made  to  sweep  the  entire  face,  returning 
by  the  numerous  roads  to  the  main-return  airways,  by  which 
it  is  conducted  to  the  foot  of  the  upcast  shaft.  Fig.  39  shows 


Overcasts  shown  thus:     X       Curtains  shown  thus: 

FIG.  39. 

a  more  extended  development  of  the  mine,  on  a  slightly  dif- 
ferent plan  from  that  given  in  the  preceding  figure. 

DISTRIBUTION  OF  AIR 

Ventilating  a  Mine. — Small  mines  are  generally   or  often 
ventilated  by  a  single  current  of  air  passing  in  one  continu- 

17 


258  MINE  GASES  AND  VENTILATION 

ous  circuit  around  the  mine.  In  larger  mines  the  main 
current  entering  the  mine  is  divided  into  two  or  more  currents 
or  "  air  splits,"  as  they  are  called. 

The  current  flowing  into  a  mine  or  section  of  a  mine  is 
called  the  "intake  current"  and  that  passing  out  from  the  mine 
the  "return."  Likewise,  these  airways  are  termed  the  "in- 
take" and  the  "return"  airways  respectively. 

The  figures  previously  given  show  clearly  the  general  ar- 
rangement of  the  circulation  in  a  mine,  as  indicated  by  the 
arrows.  In  a  gassy  mine,  the  hoisting  shaft  is  made  the  down- 
cast and  the  main-haulage  road  is  then  the  intake  airway. 
The  mine  is  ventilated  by  an  exhaust  fan  located  at  the  upcast 
shaft,  because  it  is  impracticable  to  use  a  blower  fan  whenever 
the  main-haulage  road  is  made  the  intake.  A  blower  fan 
would  require  doors  placed  on  the  haulage  road,  at  the  shaft 
bottom,  to  prevent  the  air  short-circuiting  and  passing  out 
through  the  hoisting  shaft.  All  crosscuts,  except  those 
through  which  the  air  must  pass,  are  closed  by  stoppings  or 
doors.  By  this  means,  the  air  current  is  forced  to  travel  cer- 
tain airways  from  the  downcast  to  the  upcast  shaft. 

In  Figs.  36  and  37,  the  hoisting  shaft  is  the  upcast  and  the 
haulage  road  the  return.  The  air  is  first  split  near  the  foot 
of  the  downcast  shaft.  One  current  or  split  travels  north  to 
ventilate  that  side  of  the  mine,  while  the  other  current  travels 
in  the  opposite  direction  to  ventilate  the  south  side  of  the  mine. 
Each  of  these  currents  is  shown  returning  to  the  upcast  shaft 
by  the  main  return  air-course.  Double  doors  are  used  in  the 
crosscut  at  the  shaft  bottom  to  prevent  the  air  current  from 
being  broken  or  staggered,  when  it  is  necessary  to  pass  through 
this  crosscut.  Only  one  of  these  doors  is  open  at  a  time,  and 
the  air  is  thus  prevented  from  short-circuiting  at  this  point. 

On  the  main  south  (Fig.  37),  the  air  is  divided  into  three 
separate  splits  or  currents,  which  ventilate  respectively  the 
main  south  headings,  the  first  and  second  east  and  the  first 
and  second  west.  In  order  to  do  this,  two  overcasts  are  re- 
quired, one  to  conduct  the  main-south  intake  current  over  the 
first-west  haulage  road,  and  the  other  to  carry  the  second-east 
intake  current  over  the  main-south  haulway.  It  should  be 


PRACTICAL  VENTILATION 


259 


observed  that  the  stables,  in  both  Fig.  36  and  37,  are  venti- 
lated by  a  separate  scale  of  air,  which  is  then  carried  directly 
into  the  main  return  and  passes  out  of  the  mine  as  indicated 
by  the  arrows. 

Ventilation  of  Cross-entries. — In  the  illustration  (Fig.  40) 
are  shown  two  ways  of  ventilating  a  pair  of  cross-entries 
turned  off  the  main  headings.  As  shown  on  the  left,  the 
main-intake  current  is  deflected  into  the  cross-entries  by 
placing  a  door  on  the  main  heading.  The  total  current  is  thus 
made  to  pass  down  the  first  cross-entry  and,  returning  through 
the  second  by  a  crosscut  at  the  face,  continues  on  its  way  up 
the  main  heading,  thus  forming  one  continuous  current. 


FIG.  40. 

In  the  plan  shown  on  the  right  in  the  same  figure,  the  main- 
intake  current  is  divided  at  the  mouth  of  the  first  cross-entry. 
Part  of  the  air  enters  the  first  cross-entry  and  returning  by 
the  second  passes  over  the  air  bridge  at  its  mouth  and  through 
the  crosscut  into  the  main-return  air-course.  The  remainder 
of  the  main  intake  current  continues  up  the  main  heading, 
passing  under  the  air  bridge  on  its  way.  This  method  fur- 
nishes a  separate  current  for  each  district  of  the  mine  and 
leaves  the  main  haulage  road  unobstructed  by  any  doors.  As 
shown  in  the  figure,  an  inclined  crosscut,  called  a  "  crossover," 
connects  the  two  cross-entries  near  their  mouth,  which  permits 
the  coal  from  the  back  entry  to  reach  the  main  haulage  road 
by  passing  through  the  door  on  the  crossover.  This  door 
divides  the  intake  from  the  return  on  these  entries. 


260 


MINE  GASES  AND  VENTILATION 


Ventilation  of  the  Mine  Stable. — The  mine  stable,  as  pre- 
viously stated,  should  be  ventilated  by  a  small  split  commonly 
caled  a  "scale"  of  air,  taken  from  the  main  intake  current. 
This  current,  after  ventilating  the  stables,  passes  directly  to 
the  upcast  shaft,  without  contaminating  the  air  of  the  mine. 
It  is  important  to  locate  underground  stables  so  that  they  can 
be  ventilated  (Figs.  36,  37)  with  a  small  scale  of  air  that  is 
conducted  at  once  into  the  main  return  air-course.  To  make 
possible  the  rescue  of  the  animals  in  case  of  accident,  and  to 


FIG.  41. 


facilitate  the  handling  of  feed  and  refuse  to  and  from  the  sur- 
face, the  stables  should  be  located  near  the  bottom  of  the 
hoisting  shaft  or  other  opening. 


SPLITTING  AIR  CURRENTS 

Illustration  of  Air  Splitting. — Fig.  41  gives  a  diagrammatic 
perspective  of  a  mine  ventilated  by  two  primary  air  splits, 
A  and  B,  and  two  secondary  splits,  C  and  D.  In  this  case 
either  the  downcast  or  the  upcast  may  be  made  the  hoisting 


PRACTICAL  VENTILATION 


261 


shaft,  as  desired.  In  gassy  mines  where  haulage  is  performed 
on  the  intake  air,  the  downcast  becomes  the  hoisting  shaft, 
which  avoids  the  use  of  doors  on  the  shaft  bottom.  In  that 
case,  the  air  bridges  are  constructed  to  conduct  the  return 
air  over  the  intake  current,  thus  leaving  the  haulage  road 
unobstructed. 

SYSTEMS  OF  VENTILATION 

Exhaust  vs.  Blowing  System  oi  Ve:  Dilation. — The  natural 
or  physical  conditions  that  exist  in  a  mine  will  generally 
determine  whether  it  should  be 
ventilated  on  the  exhaust  or  the  j 
blowing  system.  A  mine 
generating  gas  in  sufficient 
quantity  to  make  the  main- 
return  airway  unsafe  for  haulage 
will  require  the  exhaust  system, 
in  order  to  leave  the  hoisting 
shaft,  which  would  then  be  the 
downcast,  and  the  shaft  bottom  unobstructed  by  doors. 

The  exhaust  system  of  ventilation  is  illustrated  in  Fig.  42, 
which  shows  the  circulation  in  a  section  or  district  where 


FIG.  42. 


FIG.  43. 

the  future  development  of  a  pair  of  cross-entries  warrants 
the  building  of  an  overcast  on  the  main  headings,  and  haulage 
must  be  performed  on  the  intake  air. 

As  indicated  by  the  arrows  in  the  figure,  a  curtain  hung 
on  the  first  cross-entry,  just  inby  from  the  mouth  of  the  first 


262 


MINE  GASES  AND  VENTILATION 


room  working,  deflects  the  air  into  the  rooms  so  that  the 
major  portion  of  the  current  sweeps  the  face  of  each  room. 
It  is  necessary  also  to  hang  canvas  at  the  mouth  of  each  room 
except  the  last  to  keep  the  air  at  the  working  face. 

The  blowing  system  of  ventilation  is  illustrated  in  Fig.  43 
which  shows  the  general  arrangement  under  conditions  similar 
to  those  just  described,  except  that  here  the  haulage  is  per- 
formed on  the  return  air,  the  hoisting  shaft  being  the  upcast. 
As  indicated  by  the  arrows,  the  air  is  carried  directly  to  the 
head  of  the  cross-entries  and  returned  through  the  crosscuts 
in  the  rooms. 


SYSTEMS  OF  MINE  AIRWAYS 

The  Main  Airways.  —  While  two  airways,  an  intake  and  a 
return  airway  of  sufficient  size,  furnish  the  necessary  means 


FIG.  44. 


for  conducting  the  air  current  to  and  from  the  working  faces 
of  the  mine,  there  are  other  considerations  of  economy  and 


PR  A  CTICAL  YEN  TIL  A  TION 


203 


safety  of  operation  that  frequently  demand  a  larger  number  of 
main  airways. 

Single-entry  System. — In  the  early  days  of  mining  and  in 
some  small  mines,  today,  supplying  local  trade,  the  plan  is 
adopted  of  driving  a  single  entry,  which  serves  the  double 
purpose  of  haulage 
road  and  air- 
course,  the  air 
being  returned 
through  the  rooms. 
T  h  e  single-entry 
system  is  unsafe 
and  no  longer  used 
in  scientific  mining. 

Double-entry 
System. — In  this 
system,  all  entries 
are  driven  in  pairs, 
one  entry  being 
made  the  intake 
and  the  other  the 
return,  in  each  pair. 
This  system  is  com- 
monly employed  in 
a  large  majority  of 
coal  mines  and  is 
shown  on  the  cross- 
entries  in  Fig.  44. 

Triple-entry 
System. — In  this 
system,  three  parallel  entries  are  driven  abreast,  as  for  example 
the  main  entries  in  Fig.  44,  and  the  same  in  Fig.  45,  which 
illustrates  the  workings  in  a  slope  mine.  The  main  slope 
haulage  road  being  the  intake  for  the  entire  mine,  and  the 
air-course  on  either  side  being  the  return  for  that  respective 
side  of  the  mine.  In  the  use  of  the  triple-entry  system,  the 
center  entry  is  generally  made  the  intake  and  haulage  road, 
while  the  two  side  entries  are  the  return  air-courses  for  each 
respective  side  of  the  mine. 


FIG.  45. 


264 


MINE  GASES  AND  VENTILATION 


In  the  slope  mine  illustrated  in  Fig.  45,  the  rooms  are  driven 
to  the  rise  of  each  pair  of  gangway  headings.  The  mine  is 
equipped  with  two  ventilating  fans  operating  on  the  exhaust 


FIG.  46. 


system.  The  air  is  split  and  overcast  at  each  pair  of  headings 
on  the  right  of  the  slope,  except  the  last;  while  there  are  but 
two  air  splits  ventilating  the  levels  on  the  left  of  the  slope 


PRACTICAL  VENTILATION  265 

headings.  Unfortunately  for  purposes  of  rescue  and  handling 
feed  and  refuse,  the  mine  stable  is  located  far  in  the  workings, 
probably  to  av.oid  the  necessity  of  driving  the  mules  to  and 
from  the  working  face. 

Multiple-entries. — In  Fig.  46  is  shown  a  mine  opened  on  the 
five-entry  system  for  the  main  headings,  thus  providing  three 
intake  airways  and  two  separate  return  airways,  one  for  each 
side  of  the  mine. 

The  number  of  main  airways  required,  in  any  case,  is  de- 
termined by  their  size  and  the  necessary  volume  of  air  that 
must  pass  through  them.  The  limiting  factor  in  this  calcu- 
lation is  the  safe  and  economic  velocity  of  the  air  current 
traveling  the  main  airways. 

While  too  low  a  velocity  of  the  air  is  dangerous  because 
of  its  failure  to  remove  the  accumulating  gases,  too  high  a 
velocity,  on  the  other  hand,  is  dangerous  by  reason  of  its 
increasing  explosive  conditions  in  the  mine  air,  by  raising 
and  carrying  in  suspension  fine  dust,  and  by  furnishing  an 
excessive  supply  of  oxygen  that  invites  active  and  explosive 
combustion. 

The  velocity  of  main  air  currents  in  mines  can  safely  vary 
between  250  and  1200  ft.  per  min. :  and  for  short  distances  a 
velocity  of  2000  ft.  per  min.  may  be  permitted,  although  high 
velocities  rapidly  increase  the  power  producing  the  circulation. 
Where  the  main  intake  airways  are  used  for  haulage  roads, 
it  will  not  be  possible  or  advisable  to  employ  a  velocity  much 
exceeding  400  or  500  ft.  per  min.,  owing  to  the  annoyance 
and  danger  of  drivers  losing  their  lights. 

Economy  of  Multiple  Main  Airways. — The  economy  of 
driving  a  multiple  system  of  main  airways  will  not  be  ques- 
tioned in  the  planning  of  large  operations.  The  same  plan 
should  be  applied  to  the  opening  of  mines  on  a  smaller  scale, 
the  objective  point  being  to  keep  the  velocity  of  the  main  air 
current  so  that  it  will  not  exceed  1200  ft.  per  min.,  for  any 
considerable  distance. 

The  saving  in  power  (fuel  consumption,  equipment  and  at- 
tendance) will  pay  for  the  increased  expense  of  upkeep  of 
entries;  and  the  system  affords  a  large  increase  in  safety 


200  MINE  GASES  AND  VENTILATION 

by  reducing  explosive  conditions  and  providing  additional 
avenues  of  escape  in  case  of  accident.  There  is  afforded, 
besides,  room  for  a  double-track  haulage  system,  which  will 
prove  a  great  advantage  in  the  operation  of  the  mine. 

Assuming  that  one-half  the  power  on  the  air  is  consumed 
in  the  main  airways,  which  more  or  less  closely  approxi- 
mates the  fact,  and  taking  the  general  efficiency  of  the  fan 
and  engine  as  60  per  cent.,  a  double-entry  system,  for  the 
main  intake  and  return  airways,  would  effect  a  saving  in  fuel 
of  11.25  per  cent.;  a  triple-entry  system,  13.32  per  cent.,  and 
a4-entry  system,  14.10  per  cent. 

Illustration. — -In  the  planning  of  a  mine  for  an  output  of, 
say  2000  tons  of  coal  per  working  day,  in  a  6-ft.  seam  of  more 
or  less  inflammable  bituminous  coal  (shaft,  slope  or  drift 
openings),  the  following  data  may  be  assumed  as  approxi- 
mating possible  conditions,  but  must  be  modified  to  suit  known 
facts  that  have  been  determined,  in  special  cases: 

Output  per  man  per  day  (average) 2U  tons 

Number  of  miners  employed  (2000  -7-2.5) 800 

Number  of  loaders  or  helpers • 400 

Number  of  drivers,  trackmen,  timbermen,  etc .        60 

Foreman,  assistant  foremen  and  firebosses .        20 

Total  number  of  men  and  boys 1280 

Number  of  mules 25 

Assuming  a  gaseous  mine  requiring,  by  law,  say  150  cu.  ft. 
of  air  per  man,  and  600  cu.  ft.  per  mule,  per  minute,  the  neces- 
sary circulation  based  on  these  data  would  be  (1280  X  150)  + 
(25  X  600)  =  207,000  cu.  ft.  per  min.;  or,  to  allow  for  .certain 
leakage,  say  the  necessary  air  volume  is,  in  this  case,  225,000 
cu.  ft.  per  min. 

Driving  10-ft.  openings  in  a  6-ft.  seam  and  allowing  for 
necessary  timbering  would  leave  an  unobstructed  effective 
area  of,  say  50  sq.  ft.  In  this  case  adopting  a  4-entry  system 
for  the  intake  and  the  same  for  the  return,  would  give  for 
the  total  effective  intake  and  return  areas,  each  4  X  50  = 
200  sq.  ft.,  which  would  make  the  velocity  of  the  intake  air 


PRACTICAL  VENTILATION  267 

current  225,000  4-  200  =  1125ft.  per  min.,  which  is  a  safe 
and  economical  velocity,  provided  these  airways  are  not  used 
as  haulage  roads. 

To  provide  for  the  expansion  of  the  return  air,  owing  to 
rise  of  temperature  and  addition  of  mine  gases,  which  may 
altogether  amount  to  6  or  8  per  cent.,  the  return  airways 
should  be  driven,  say  8  or  10  in.  wider  than  the  intake  air- 
ways. 


SECTION  VIII 
MINE  LAMPS  AND  LIGHTING 

PRINCIPLES  OF  CONSTRUCTION,  CLASSIFICATION  OF  SAFETY 
LAMPS,  REQUIREMENTS — CHARACTERISTIC  TYPES  OF  LAMPS 
— SPECIAL  TYPES  OF  SAFETY  LAMPS — PERMISSIBLE  MINE 
SAFETY  LAMPS — USE  AND  CARE  OF  SAFETY  LAMPS — TESTING 
FOR  GAS  BY  INDICATORS — THE  FLAME  TEST — ILLUMINANTS 
FOR  SAFETY  LAMPS,  OILS,  ETC. — MINERS'  CARBIDE  LAMPS — 
ELECTRIC  MINE  LAMPS— PERMISSIBLE  PORTABLE  ELECTRIC 
MINE  LAMPS. 

A  volume  could  be  written  on  the  development  of  the  so- 
called  "safety  lamp."  It  is  not  proposed  to  give,  here,  the 
history  of  that  development  further  than  to  say  that  it  began 
with  the  discovery  of  the  two  most  important  and  essential 
principles  of  all  mine  safety  lamps.  Strange  to  say,  these 
two  principles  were  discovered  at  practically  the  same  time 
and  by  two  men  of  different  education  and  calling. 

PRINCIPLES  OF  CONSTRUCTION 

Principle  of  Protecting  Shield. — George  Stephenson  was  a 
practical  miner  of  considerable  mechanical  ability,  which  led 
him  into  the  practice  of  cleaning  and  repairing  watches  and 
clocks,  running  engines  and  performing  other  similar  services. 
It  was  at  the  Killingworth  colliery,  Oct.  21,  1815,  that  he 
made  the  first  trial  of  a  lamp  he  had  devised  for  use  in  mines 
generating  gas. 

The  principle  of  the  Stephenson  lamp  consisted  in  confining 
the  burnt  air  and  products  of  combustion  in  the  upper  portion 
of  the  lamp  chimney  or  bonnet,  the  idea  being  that  this  would 
furnish  an  extinctive  atmosphere  at  the  top  of  the  lamp  and 
prevent  the  flame  of  the  burning  gases  passing"  out  of  the 
chimney  and  igniting  the  gas-charged  air  surrounding  the 
lamp.  This,  today,  is  one  of  the  important  principles  of  all 

268 


MINE  LAMPS  AND  LIGHTING 


269 


mine  safety  lamps,  though  the  method  of  its  application  differs 
from  that  employed  by  Stephenson. 

Principle  of  Wire  Gauze. — The  principle  of  the  isolation  of 
a  lamp  flame,  by  means  of  a  wire  gauze  envelope  or  chimney, 
was  discovered  by  Sir  Humphry  Davy,  an  eminent  chemist. 
As  the  result  of  a  series  of  experiments,  Davy  was  able,  Dec. 
15,  1815,  to  announce  to  the  world  the  fact,  that  an  ordinary 
lamp  flame  will  not  pass  through  the  mesh  of  cool  wire  gauze. 
The  idea  was  suggested  to  the  mind  of  Davy  by  observing 
that  a  flame,  as  shown  in  Fig.  47,  never  comes  in  direct 
contact  with  cool  metal.  The  reason  is  that  the 
temperature  of  the  burning  gas  is  reduced,  in 
close  proximity  to  the  metal,  below  the  point  of 
ignition.  He  showed  that  the  burning  gas,  on 
passing  through  the  mesh  of  a  wire  gauze,  is 
broken  up  into  tiny  streamlets,  which  are  so 
cooled  by  contact  with  the  metal  of  the  gauze 
that  the  flame  is  extinguished.  As  the  gauze 
becomes  heated  by  the  close  proximity  of  the 
flame,  however,  it  loses  its  cooling  effect  and  the 
flame  then  passes  through  the  mesh. 

The  effect  of  cool  wire  gauze  to  prevent  the 
passage  of  flame  through  its  mesh  is  shown  in 
the  lower  half  of  Fig.  48.  In  the  upper  half, 
appears  the  later  passage  ot  the  flame  through 
the  mesh  of  the  gauze  when  the  wire  has  become 
heated  so  that  it  is  unable  to  absorb  sufficient  heat  from  the 
burning  gas  to  extinguish  the  flame.  This  isolation  of  the 
flame  of  a  safety  lamp  by  means  of  a  wire  gauze  chimney 
found  its  earliest  application  in  the  Davy  lamp.  A  careful 
study  of  the  problem  and  the  experiments  performed  showed 
that  the  greatest  safety  was  secured  by  the  adoption  of  a 
standard  mesh  formed  by  28  steel  wires,  No.  28  B.w.g., 
making  784  openings  per  square  inch.  This  standard  mesh  is 
still  used  in  England  and  in  this  country,  today.  It  was  also 
found  that  the  volume  of  the  chimney,  including  the  combus- 
tion chamber  of  the  lamp,  should  bear  a  certain  relation  to 
the  surface  of  the  gauze  in  order  to  produce  the  best  results 


FIG.  47. 


270 


MINE  GASES  AND  VENTILATION 


and  insure  the  greatest  security  of  the  lamp  when  burning 
in  the  presence  of  gas.  There  is,  however,  no  fixed  value 
for  this  ratio,  which  controls  the  circulation  of  the  air  and  gas 
passing  in  and  out  of  the  lamp  and  varies  with  the  type  of 
construction. 

Classification  of  Safety  Lamps. — Mine  safety  lamps  are 
divided  into  two  general  classes,  according  to  their  use  in  the 
mine,  as  follows:  (a)  Lamps  for  testing  for  gas.  (6)  Lamps 

for  general  use  at  the 
working  face.  A 
good  working  lamp 
does  not  make  a  good 
lamp  for  testing  for 
gas,  neither  does  a 
good  testing  lamp 
answer  for  work  at 
the  face.  Each  of 
these  lamps  is  design- 
ed for  the  particular 
service  or  work  to 
-  be  performed  and  the 
requirements  of  each 


Coo)  Wire  Gauze 


FIG.  48. 


are  widely  different. 
Requirements  of  a 
Good  Testing  Lamp. 
— A  good  lamp  for 
testing  for  gas  must 
be  sensitive  to  small 
percentages  of  gas 
present  in  the  mine  air  and  must  possess,  as  nearly  as  practi- 
cable, the  same  conditions  with  respect  to  gas  in  the  combustion 
chamber  as  exist  in  the  air  surrounding  the  lamp.  Otherwise, 
the  test  for  gas  observed  within  the  lamp  will  not  correctly 
represent  the  gaseous  condition  of  the  outer  air. 

The  sensitiveness  of  a  lamp  to  gas  depends  on  both  the 
character  of  the  oil  burned  and  the  freedom  of  circulation 
within  the  combustion  chamber.  A  lamp  burning  hydrogen 
gas  (Clowes'  hydrogen  lamp)  is  more  sensitive  than  a  lamp 


MINE  LAMPS  AND  LIGHTING  271 

burning  oil,  which  is  true  in  general  of  a  gas-fed  flame.  The 
Clowes  lamp  is  the  only  safety  lamp  burning  gas,  however, 
and  has  but  a  limited  use  in  testing  for  gas  in  mines.  There  are 
two  general  types  of  oil-burning  lamps,  according  as  the 
illuminant  is  a  non- volatile  or  a  volatile  oil,  the  former  being 
derived  from  animal  or  vegetable  sources,  while  the  latter 
are  chiefly  derivatives  of  mineral  oil  or  petroleum  distilled 
below  300  deg.  F.,  such  as  naphtha,  benzine,  etc.  Coal  oil 
(kerosene)  is  a  distillate  of  petroleum  between  300  and  500  deg. 
F.,  and  is  not  classed  as  a  volatile  oil.  It  is  frequently  mixed 
with  twice  its  volume  or  more  of  a  vegetable  oil  to  improve 
the  illuminating  power  of  the  latter. 

The  volatile  oils,  while  more  sensitive  to  the  presence  of  gas, 
possess  the  disadvantage  of  giving  a  more  pronounced  oil 
or  fuel  cap  that  is  frequently  mistaken  for  a  gas  cap.  More- 
over, the  height  of  the  flame  cap,  for  any  given  percentage  of 
gas,  is  always  greater  in  a  lamp  burning  a  volatile  oil  and 
allowance  must  be  made  for  this  fact,  in  estimating  the  per- 
centage of  gas  present  when  making  the  test  with  such  a  lamp. 

In  order  that  a  lamp  shall  present  the  same  condition  with 
respect  to  gas,  within  as  exists  without  the  lamp,  two  con- 
ditions must  be  fulfilled:  (1)  The  air  must  enter  the  combus- 
tion chamber  at  a  point  below  the  flame.  (2)  There  must  be  a 
free  circulation  within  the  lamp  and  it  must  always  be  ascen- 
sional so  as  to  avoid  the  contamination  of  the  atmosphere  in 
the  combustion  chamber  with  the  products  of  combustion 
in  the  chimney,  which  are  apt  to  descend  from  the  upper  portion 
of  the  lamp  if  the  chimney  is  too  closely  bonneted  and  the 
circulation  in  the  lamp  is  not  wholly  ascensional. 

Other  requirements  of  a  good  testing  lamp  are  some  means 
of  accurately  measuring  the  height  of  the  flame  cap  formed 
in  the  lamp  and,  if  possible,  making  the  cap  more  plainly  dis- 
cernible by  means  of  a  good  background  and  the  absence  of  a 
reflection  that  would  interfere  with  the  observation.  A  good 
testing  lamp  should  also  be  provided  with  a  shield  or  suitable 
bonnet  to  protect  the  lamp  against  strong  air  currents  and  as 
an  added  protection  against  slight  explosions  that  may  occur 
within  the  lamp,  owing  to  a  body  of  strong  gas. 


272  MINE  GASES  AND  VENTILATION 

Requirements  of  a  Good  Working  Lamp. — -Unlike  the  test- 
ing lamp,  a  lamp  designed  for  general  work  in  the  mine  must 
not  be  too  sensitive  to  gas.  Its  chief  requirements  are  the 
following : 

1.  The  lamp  must  give  a  good  light  that  will  enable  the 
miner  to  perform  his  work  readily  and  discover  any  dangers 
that  may  exist  in  the  roof  or  about  him. 

2.  The  lamp  should  be  simple  in  construction,  portable  and 
light  and,  at  the  same  time,  capable  of  resisting  rough  usage 
that  is  liable  to  break  the  glass,  injure  the  gauze  or  otherwise 
damage  the  lamp.     There  should  be  as  few  parts  as  practi- 
cable, and  these  should  be  assembled  in  such  a  manner  that 
no  single  part  'can  be  accidentally  omitted  when  putting  the 
lamp  together  in  the  lamproom. 

3.  A  good  working  lamp  must  be  secure  against  strong  air 
currents.     It  should  be  suitably  protected  by  a  shield  or  bon- 
net of  such  construction  as  will  not  unduly  obstruct  the  circula- 
tion within  the  lamp.     The  best  type  of  lamp  admits  the 
air  to  the  combustion  chamber,  at  a  point  below  the  flame,  and 
allows  the  products  of  combustion  to  pass  out  through  tan- 
gential openings  in  the  bonnet.     A  shield  protects  the  top 
of  the  bonnet  from  dust  and  falling  fragments  of  the  roof. 

4.  It  is  important  that  every   working  lamp   should   be 
provided  with  a  lock  fastening  that  will  betray  any  attempt 
on  the  part  of  the  miner  to  tamper  with  the  lock.     Magnetic 
locks,  it  is  claimed  can  only  be  opened  by  means  of  a  strong 
magnet  in  the  lamproom,  but  the  claim  has  been  questioned  in 
numerous  instances,  especially  where  a  mine  is  equipped  with 
electrical  installation.     The  fastening  that  has  given,  perhaps, 
the  greatest  amount  of  satisfaction  because  of  its  simplicity 
and  security  is  the  old  lead  lock  that  is  fastened  in  the  lamp- 
room  with  a  steel  die  of  special  design. 

Working  lamps  are  supplied  with  both  round  and  flat 
burners,  as  desired.  When  a  flat  burner  is  used  the  illumina- 
tion is  much  improved  by  the  simple  device  illustrated  in  Fig. 
49,  consisting  of  a  semi-circular  cut  made  in  the  center  of 
the  top  of  the  burner.  This  simple  artifice  has  the  effect  of 
producing  a  rounder  and  less  smoky  flame,  besides  giving  a 
hotter  flame  when  the  latter  is  reduced,  in  testing  for  gas. 


MINE  LAMPS  AND  LIGHTING  273 

The  illuminating  power  of  a  safety  lamp  is  greatly  influenced 
by  the  way  in  which  the  air  supply  is  brought  into  contact  with 
the  flame  and  the  volume  of  air  supplied  to  the  combustion 
chamber  of  the  lamp.  The  light-giving  power  of  the  flame  is 
also  increased  by  the  use  of  duplex  flat-wick  tubes,  or  triplex 
round-wick  tubes.  Tin  or  aluminum  tubes  produce  a  better 
light  than  either  brass  or  copper,  and  porcelain  is  far  better 
than  any  metal,  in  this  respect. 

Increased  light  does  not  mean  an  increased  cost  in  oil. 
Petroleum  having  a  high  flashing  point,  such  as  mineral 
colza  oil,  is  probably  best  adapted  for  use  in  high-powered 
lamps.  The  illuminating  power  of  vegetable  oils  is  greatly 
increased  by  the  admixture  of  one-third  part  of  pretroleum 
(coal  oil)  having  a  flashing  point  of  80  deg.  F.,  although  the 
lamp  flame  will  then  have  a  greater  tendency 
to  smoke  and  will  require  a  better  circulation 
of  air  in  the  lamp. 

The  safety  of  gauze-protected  lamps  is  much 
increased  by  a  suitable  restriction  of  both  the 
inlet  and  the  outlet  openings,  which  is  a  promi- 
nent feature  of  many  lamps  of  high  illuminat- 
ing power.     Another  important  feature  of  these 
lamps  and  one  that  affords  increased  protection 
at  the  top  of  the  chimney  is  the  inner  metal  bonnet  sur- 
mounted by  a  truncated  cone.     Still  another  feature  that  adds 
to  the  protection  of  the  lamp  and  increases  its  illuminating 
power,  by  the  concentration  of  the  heat  in  the  combustion 
chamber,  is  the  conical  glass.     All  of  these  features  originated 
in  the  Ashworth-Gray  lamp,  a  type  of  which  was  later  styled 
the  Ashworth-Hepplewhite-Gray  lamp. 

A  working  lamp  must  be  of  a  design  that  will  make  it  most 
convenient  for  the  use  of  the  miner.  The  base  of  the  lamp 
should  be  sufficiently  broad  to  enable  the  lamp  to  be  set  on  the 
mine  bottom,  in  a  position  to  throw  a  good  light  where  the 
coal  is  being  undercut  or  mined.  It  is  often  necessary  for  the 
miner  to  hang  his  lamp  on  a  timber  or  post.  For  that  reason, 
some  lamps  are  furnished  with  a  short  hook  instead  of  the 
usual  ring  forming  the  handle.  The  hook  is  not  commonly 

18 


274  MINE  OASES  AND  VENTILATION 

used  in  this  country,  the  miner  preferring  to  hang  his  lamp  on 
a  nail  driven  in  the  timber. 

Aji  important  feature  of  a  working  lamp  is  a  good  pricker, 
which  will  enable  the  miner  to  remove  the  crust  that  forms  on 
the  top  of  the  wick  of  an  oil-burning  lamp.  The  pricker  must 
be  of  such  a  form  that  the  wick  can  be  cleaned  without  danger 
of  extinguishing  the  light. 

A  lamp  burning  a  volatile  oil,  the  most  common  form  being 
those  of  the  Wolf  type,  requires  some  kind  of  igniter,  in  the 
combustion  chamber,  to  enable  the  lamp  to  be  relit  when  acci- 
dentally extinguished.  Lamps  burning  a  volatile  oil  are  more 
subject  to  extinction,  either  from  a  sudden  jar  or  from  gas, 
than  those  burning  a  non-volatile  oil.  The  chief  objection  to 
lamp  igniters  is  the  opportunity  that  they  afford  the  curious 
miner  of  fooling  with  his  lamp. 

The  old  form  of  igniter  consisted  of  a  narrow  ribbon  of 
waxed  paper  containing  little  nubs  of  fulminate,  which  were 
ignited  by  a  rod-scraper  that  extended  up  through  the  oil 
vessel  of  the  lamp.  This  form  of  igniter  has  now  largely  given 
place  to  one  in  which  ignition  is  caused  by  the  sparks  from  a 
cerium  compound.  The  objection  to  the  wax-taper  igniter 
is  the  flame  of  the  burning  taper  and  the  charred  remains  that 
often  proves  an  annoyance  in  the  lamp,  especially  when  one 
or  more  of  the  nubs  fail  to  ignite,  which  is  frequently  the 
case. 

Specifications  by  the  Bureau  of  Mines. — -In  January,  1915, 
the  Federal  Bureau  of  Mines,  acting  under  the  authorization 
of  an  act  of  Congress  (37  Stat.,  681),  approved  Feb.  25,  1913, 
issued  "  Schedule  7,  entitled  "  Procedure  for  Establishing  a 
List  of  Permissible  Miners'  Safety  Lamps."  Following  are 
the  more  important  announcements  and  specifications  con- 
tained in  that  schedule,  which  is  still  in  force  in  relation  to  so- 
called  "  Permissible  "%  safety  lamps  for  mining  use. 

The  Bureau  of  Mines  is  prepared,  at  its  Pittsburgh  experi- 
ment station,  to  conduct  tests  of  miners'  flame  safety  lamps 
for  the  purpose  of  establishing  a  list  of  permissible  safety  lamps 
for  use  in  mines  in  which  explosive  gas  is  liberated.  This 
schedule  of  tests  is  submitted  for  the  information  of  those 


MINE  LAMPS  AND  LIGHTING  275 

who  may  desire  to  submit  a  type  of  lamp  for  test,  which  must 
fulfill  the  following  general  requirements.  (See  also,  p.  288.) 

1.  The  lamp  must  be  provided  with  double  gauzes  or  with  some 
other  adequate  arrangement  serving  the  same  purpose.     Every  gauze 
must  be  of  steel  or  best  charcoal-annealed  iron  wire,  not  larger  than  27 
Brown  &  Sharpe  gage  (0.014  in.  in  diameter),  with  28  meshes  to  the 
lineal  inch  (784  to  the  square  inch),  nor  less  than  29  Brown  &  Sharpe 
gage  (0.01125  in.  in  diameter)  with  29  meshes  to  the  lineal  inch  (841 
to  the  square  inch). 

2.  If  lamp  standards  are  used,  the  standards  must  be  so  arranged 
that  a  straight  line  touching  the  exterior  part  of  any  two  consecutive 
standards  will  not  touch  the  glass. 

3.  The  lamp  must  be  so  constructed  that  it  will  not  be  possible  with- 
out easy  detection  to  assemble  the  component  parts  of  the  lamp  without 
the  gauze. 

4.  The  lamp  must  be  provided  with  an  efficient  locking  device  to 
prevent  the  fuel  vessel,  glass,  or  bonnet  from  being  removed  by  un- 
authorized persons,  or  being  loosened  to  such  an  extent  that  the  safety 
of  the  lamp  is  impaired.     Provision  shall  also  be  made  for  taking  up  the 
play  due  to  wear  of  the  screw  threads. 

5.  The  glass  globes  shall  have  their  two  ends  as  nearly  parallel  as  it 
is  practicable  to  make  them. 

6.  The  lamp  will  be  examined  in  respect  to  its  general  design,  strength, 
and  general  character  of  construction. 

CHARACTERISTIC  TYPES  OF  LAMPS 

The  purpose,  in  this  volume,  is  to  show  the  general  develop- 
ment of  the  safety  lamp,  by  explaining  those  characteristic 
features  that  form  the  most  essential  elements  of  all  safety 
lamps.  It  would  be  useless  to  attempt  to  describe  in  detail 
the  construction  of  the  many  different  lamps  now  on  the  mar- 
ket, as  such  a  description  would  not  be  instructive  in  the  way  of 
demonstrating  what  features  are  essential  in  securing  the  high- 
est efficiency  and  a  maximum  degree  of  security  in  the  lamp. 
While  the  number  of  different  safety  lamps  in  use  are  legion, 
there  are  a  comparatively  few  that  are  characteristic  of  the 
essential  features  that  promote  safety  in  the  use  of  the  lamp. 

The  Davy  Lamp. — This  is  one  of  the  early  types  of  safety 
lamps  that  still  survives.  The  common,  unbonneted  Davy 
is  shown  in  the  illustration,  Fig.  50  and  consists  of  a  brass 


276 


MINE  GASES  AND  VENTILATION 


or  aluminum  oil  vessel  surmounted  by  a  wire-gauze  chimney 
of  standard  mesh.  Three  round  iron  or  brass  rods,  called  the 
" standards"  of  the  lamp,  are  attached  to  the  oil  vessel  and 
carry  a  brass  ring  that  furnishes  the  upper  support  of  the 
gauze  chimney.  Above  the  ring  is  a  cap  or  shield  of  brass  to 
which  is  attached  the  handle  for  holding  the  lamp. 

There  are  several  forms  of  the  Davy  lamp  known,  respec- 
tively, as  the  "fireboss  Davy,"  " pocket  Davy,"  etc.  The 

common  Davy  has  a  single,  gauze 
chimney,  in  the  form  of  a  straight 
cylinder  I^{Q  in.  in  diameter  and 
varying  fro'm  4%  to '6  in.  in  height. 
The  type  known  as  the ' '  pocket  Davy  " 
is  somewhat  smaller  and  the  height 
of  its  gauze  is  reduced  to  4  in.  One 
form  of  the  Davy  lamp  that  was 
much  used  in  England  had  a  glass 
cylinder  surrounding  the  lower  portion 
of  the  gauze  chimney,  while  a  steel 
bonnet  enclosed  the  top  of  the  chim- 
ney. Openings  were  provided  in  the 
top  of  the  bonnet  for  the  escape  of  the 
gases  and  burnt  air  formed  in  the 
lamp.  Other  forms  used  in  England 
were  the  " tin-can  Davy,"  having  a 
metal  shield  covering  the  entire  gauze 
chimney.  This  shield  was  provided 
with  openings  for  the  circulation  of 
the  air  and  a  glass  window  for  observ- 
ing the  indications  of  the  lamp.  In  the  "Davy  with  glass 
shield"  the  metal  shield  was  replaced  with  a  glass  cylinder 
that  extended  the  full  height  of  the  gauze  chimney.  The 
"jack  Davy"  was  a  small  sized  lamp  corresponding  to  the 
pocket  Davy  used  in  this  country. 

The  Davy  lamp  is  designed  to  burn  sperm,  cottonseed, 
or  lard  oil.  Owing  to  the  free  circulation  of  air  passing  in  and 
out  of  the  lamp,  the  unbonneted  Davy  is  a  favorite  among 
firebosses  in  this  country.  It  is  extremely  sensitive  to  gas, 


FIG.  50. 


MINE  LAMPS  AND  LIGHTING 


277 


and,  on  this  account,  flames  readily  when  exposed  to  a  con- 
siderable body  of  gas.  Owing  to  its  sensitiveness  to  gas  and 
the  dim  light  afforded,  the  Davy  is  not  a  safe  or  suitable 
working  lamp.  Its  use  for  that  purpose  is  prohibited  by  the 
mining  laws  of  some  states.  The  unbonneted  Davy  lamp  is 
unsafe  in  a  current  having  a  velocity  exceeding  6ft.  per  second. 
The  Clanny  Lamp.— The  illustration,  Fig.  51,  shows  the 
common  form  of  Clanny  lamp,  unbonneted  and  bonneted. 


FIG.  51. 

In  this  lamp  the  brass  oil  vessel  is  surmounted  by  a  glass 
cylinder  above  which  is  the  wire-gauze  chimney.  The  glass 
of  the  Clanny  lamp  enables  it  to  give  a  better  light  than  the 
Davy.  The  lamp  is  less  sensitive  to  gas  and  more  or  less 
liable  to  smoke,  however,  because  the  air  must  enter  the  lamp 
above  the  glass,  through  the  lower  portion  of  the  gauze 
chimney  and  descend  to  the  flame,  which  causes  a  conflict 
of  the  descending  and  ascending  currents  of  air,  in  the  com- 
bustion chamber  of  the  lamp. 


278 


MINE  GASES  AND  VENTILATION 


Owing  to  the  simplicity  of  its  construction,  the  bonneted 
Clanny  lamp  is  largely  used  as  a  working  lamp,  in  many  mining 
districts.  Improved  types  of  the  Clanny  lamp  have  been 
introduced,  from  time  to  time,  by  different  manufacturers. 
Some  of  these  have  adopted  the  principle  of  the  early  Eloin 
lamp,  by  which  the  air  entered  the  combustion  chamber  of 
the  lamp  at  a  point  below  the  flame.  This  construction  is 
known  as  the  "Eloin  principle"  of  safety  lamps.  By  this 
means,  the  tendency  of  the  lamp  to 
smoke  is  reduced  to  a  minimum. 

The  Clanny  lamp  is  designed  to  burn 
sperm,  cottonseed,  or  lard  oil.  It  is 
equipped  either  with  the  round  or  the 
flatwick  burner  and  the  usual  pricker  for 
cleaning  and  raising  or  lowering  the  wick 
in  the  wick  tube.  The  illuminating 
power  of  different  types  of  Clanny  lamps 
varies  from  0.25  to  0.50  cp.  While  the 
unbonneted  Clanny  lamp  becomes  unsafe 
in  a  current  velocity  exceeding  8  ft.  per 
sec.,  different  types  of  this  lamp  when 
bonneted  have  been  able  to  withstand 
current  velocities  varying  from  1200  to 
1500  ft.  per  min.,  and,  in  a  few  cases, 
certain  lamps  of  this  type  have  not  failed 
when  the  velocity  has  been  increased  to 
2000  ft.  per  min.,  but  this  must  be  re- 
garded as  exceptional. 
The  Marsaut  Lamp. — This  lamp  differs  in  no  respect  from 
the  Clanny  lamp  just  described,  with  the  one  exception 
that  the  single-gauze  chimney  of  the  Clanny  lamp  is  here 
replaced  by  two  or  three  concentric  conical  gauzes  forming  the 
chimney  of  the  lamp.  This  feature  is  clearly  seen  in  the  illus- 
tration, Fig.  52,  which  shows  an  unbonneted  Marsaut  lamp 
having  a  conical  gauze  within  the  cylindrical  gauze  forming 
the  chimney  of  the  lamp.  The  double-gauze  chimney  is  the 
characteristic  feature  of  the  Marsaut  type. 

The  multiple  gauzes  give  protection  to  the  upper  portion  of 


FIG.  52. 


MINE  LAMPS  AND  LIGHTING  279 

the  lamp.  The  top  of  a  lamp  chimney,  where  the  heat  is 
concentrated,  always  presents  the  greatest  danger  of  the  trans- 
mission of  the  flame  through  the  gauze.  This  fact  is  recog- 
nized in  the  construction  of  both  the  Davy  and  Clanny  lamps 
by  providing  a  gauze  cap,  which  serves  as  a  means  for  the 
better  protection  of  that  point. 

The  lamp  shown  here  is  a  modified  type  of  Marsaut,  de- 
signed on  the  "Eloin"  principle  of  admitting  the  air  below  the 
glass,  which  improves  the  circulation  and  the  illuminating 
power  of  the  lamp.  This  type  is  known  as  the  "  Beard 
Deputy7'  and  contains  the  Beard-Mackie  Sight  Indicator, 
described  later  (see  p.  297). 

The  Marsaut  principle  of  multiple  wire-gauze  chimneys 
has  been  found  particularly  applicable  to  lamps  designed 
on  the  Eloin  principle,  where  the  air  is  admitted  to  the  com- 
bustion chamber  of  the  lamp  at  a  point  below  the  flame,  which 
increases  the  air  column  or  the  upward  draft  in  the  lamp. 

One  type  of  double-gauze  Marsaut  lamp,  bonneted,  when 
tested,  was  found  to  be  safe  in  an  explosive  mixture  having  a 
velocity  of  2600  ft.  per  min.,  while  a  triple-gauze  lamp  of 
this  type  withstood  a  current  velocity  of  3100  ft.  per  min. 

The  illuminating  power  of  the  double-gauze  lamp,  burning 
sperm  oil,  was  found  to  be  0.70  cp.;  but,  in  the  triple-gauze 
Marsaut,  this  was  reduced  to  0.50  cp. 

The  Mueseler  Lamp. — The  special  feature  of  this  lamp  that 
is  characteristic  is  the  central  conical  sheet-iron  chimney, 
supported  with  its  mouth  a  short  distance  above  the  tip  of  the 
flame  of  the  lamp  and  concentric  within  the  wire-gauze 
chimney,  as  shown  in  the  illustration,  Fig.  53.  The  other 
features  of  the  Mueseler  lamp  are  similar  to  those  of  the 
Clanny  lamp,  except  that  the  height  of  the  glass  cylinder 
is  somewhat  reduced  and  the  lamp  is  provided  with  a  deflector 
surrounding  and  supporting  the  metal  chimney  and  directing 
the  air  as  it  enters  the  lower  portion  of  the  wire-gauze  chimney. 

The  chief  effect  of  the  metal  chimney  of  the  Mueseler  lamp 
is  the  increased  protection  afforded  against  explosion  within 
the  lamp,  by  separating  the  descending  and  ascending  air 
currents.  Although  the  inner  chimney  improves  the  circula- 
tion, the  illuminating  power  of  the  lamp  is  decreased. 


280 


MINE  GASES  AND  VENTILATION 


The  Mueseler  principle,  however,  presents  the  advantage  of 
increasing  the  security  of  the  lamp  against  internal  explosions. 
The  shape  of  the  central  chimney  is  conical,  corresponding  to 
that  of  the  gauze  chimney  above  it.  When  the  lamp  is 
exposed  to  a  body  of  sharp  gas,  and  slight  explosions  occur  in 
the  combustion  chamber  of  the  lamp,  the  force  of  these  ex- 
plosions is  broken  by  the  solid  metal  chimney,  and  the  danger 
of  flame  being  transmitted  through  the  wire  gauze  is  much  less 
than  where  the  gauze 'chimney  must  withstand  the  full  force  of 
the  explosion  within  the  lamp.  This  has  always  been  con- 


FIG.  53. 

sidered  as  an  important  principle  in  safety  lamp  construction. 
For  some  reason,  however,  the  Mueseler  principle  has  not 
been  generally  adopted  in  the  manufacture  of  safety  lamps 
in  this  country; 

There  are  two  types  of  the  Mueseler  lamp,  known  as  the 
English  Mueseler,  shown  on  the  right  in  Fig.  53,  and  the 
Belgian  Mueseler,  shown  on  the  left.  These  types  differ 
only  in  the  dimensions  of.  the  central  sheet-iron  chimney. 
The  Belgian  chimney  is  taller  and  narrower  than  that  of  the 
English  type.  The  tests  of  these  two  types  of  Mueseler  have 


MINE  LAMPS  AND  LIGHTING  281 

shown  that  the  Belgian  lamp  is  superior  to  the  English  type. 
The  former  successfully  withstood  a  current  velocity  of  over 
2800  ft.  per  min.,  while  the  English  lamp  failed  at  a  velocity 
of  1000  ft  per  min.,  the  explosive  condition  of  the  current 
being  the  same  in  each  case. 

The  original  Mueseler  type  of  safety  lamp  has  a  horizontal 
wire-gauze  diaphragm,  at  the  base  of  the  gauze  chimney. 
This  diaphragm  separates  the  air  in  the  combustion  chamber 
from  that  within  the  gauze  chimney  above,  except  for  the 
opening  provided  through  the  central  metal  chimney.  The 
failure  of  the  English  Mueseler  at  a  comparatively  low  velocity 
was  probably  due  to  the  short  and  broad  metal  chimney 
of  that  lamp,  which  provided  an  ample  passage  between  the 
combustion  chamber  and  the  gauze  chimney  above.  The  effect 
of  this  was  to  counterbalance  the  protection  afforded  by  the 
gauze  diaphragm  separating  these  two  compartments  of  the 
lamp. 

The  Mueseler  chimney, -as  stated,  in  spite  of  its  advantage 
in  increasing  the  security  of  the  lamp,  possesses  the  disadvan- 
tage of  decreasing  its  illuminating  power,  which  is  only  from 
0.20  to  0.40  cp.  This  type  of  lamp  also  possesses  the  dis- 
advantage that  it  must  be  held  in  an  erect  position,  as  only  a 
slight  deviation  from  the  vertical  interferes  so  seriously  with 
the  circulation  through  the  central  chimney  as  to  give  op- 
portunity for  gas  that  accumulates  between  the  gauze  chimney 
and  the  central  tube,  to  enter  the  combustion  chamber. 
From  this  cause,  explosions  have  resulted  within  the  lamp  and 
caused  its  failure.  Owing  to  the  same  conditions  requiring 
the  lamp  to  be  held  in  a  vertical  position,  its  flame  is  easily 
extinguished  by  the  burnt  air  and  gases  drawn  into  the  combus- 
tion chamber  from  the  gauze-chimney  above. 

SPECIAL  TYPES  OF  SAFETY  LAMPS 

Under  the  head  of  Special  Lamps .  may  be  classed  those 
designed  for  a  special  purpose  only,  such  as  testing  for  gas 
for  example,  the  Pieler,  the  Chesneau,  the  Ashworth,  Stokes, 
and  the  Clowes  hydrogen  lamps,  besides  lamps  of  the  Wolf 


282 


MINE  GASES  AND  VENTILATION 


type  designed  to  burn  a  volatile  oil  and  the  Beard-Deputy, 
with  the  B-M  sight  indicator  attachment  for  measuring  small 
percentages  of  gas  with  accuracy.  These  lamps  will  be 
treated  briefly,  being  modifications  of  the  original  types  of 
safety  lamp  described  previously. 

The  Pieler  Lamp. — This  is  a  special  Davy  lamp  designed  to 
burn  alcohol  and  used  for  the  purpose  of  testing  for  gas.  The 
alcohol  flame,  as  is  well  known,  is  sensitive  to  gas  to  a  high 

degree  The  presence  of  Y±  of  1 
per  cent,  of  gas  in  the  air  entering 
the  lamp  elongates  the  alcohol  flame 
to  a  height  of  3.2  in.,  while  1  J^>  per 
cent,  of  gas  lengthens  the  flame  hi 
the  Pieler  lamp  to  a  height  close 
to  7  in.  Larger  percentages  of  gas 
than  this  cause  the  lamp  to  flame 
and  makes  its  use  very  dangerous 
in  coal-mining  practice.  In  making 
a  test  for  gas  with  this  lamp  the 
flame  is  first  adjusted  so  that  its  tip 
reaches  the  top  of  the  conical  shield 
that  surrounds  the  flame.  The 
height  of  this  flame  is  2  in. 

Owing  to  the  free  circulation  of 
air  in  the  Pieler  lamp,  as  in  the 
original  Davy,  and  the  lengthening 
of  the  alcohol  flame,  the  gauze- 
chimney  of  the  Pieler  lamp,  as 
shown  in  the  illustration,  Fig.  54,  is  increased  to  a  height  of 
7.5  in.  and  made  slightly  conical.  The  lamp  has  four  stand- 
ards and  is  provided  with  a  screen  having  horizontal  slots 
through  which  the  height  of  the  flame  cap  is  observed  and 
measured.  This  screen  is  attached  to  two  of  the  standards 
of  the  lamp  in  a  fixed  position. 

A  slightly  conical  metal  hood  surrounds  the  flame  of  the 
lamp  and  is  of  such  height  that  the  tip  of  the  ordinary  alcohol 
flame  just  reaches  the  top  of  this  hood.  At  times,  the  Pieler 
lamp  is  bonneted,  in  which  case  a  glass  window  is  provided 


FIG.  54. 


MINE  LAMPS  AND  LIGHTING 


283 


extending  the  full  height  of  the  bonnet  and  marked  with  a 
scale  for  measuring  the  observed  height  of  the  flame  in  gas. 

The  Chesneau  Lamp. — This  lamp  is  very  similar  to  the 
Pieler  lamp  just  described,  except  in  a  few  details  of  construc- 
tion. The  lamp  is  bonneted  and  the  air  enters  the  lamp 
through  double-gauze  openings  at  the  bottom  of  the  chimney. 
A  hollow  sheet-metal  cylinder  surrounds  the  flame  and  sup- 
ports the  small  gauze  chimney,  its  purpose  being  similar  to 
that  of  the  metal  one  in  the  Pieler  lamp. 
Like  the  Pieler,  the  Chesneau  lamp  is 
designed  to  burn  alcohol.  In  both  of 
these  lamps  cotton  is  inserted  in  the  oil 
vessel  for  the  purpose  of  absorbing  the 
alcohol  and  preventing  leakage  in  case 
the  lamp  is  overturned.  However,  the 
absorptive  power  of  the  cotton  is  suf- 
ficiently strong  to  modify  the  height  of 
the  flame  and  affect  the  accuracy  of  the 
determination  of  percentage. 

Ashworth-Hepplewhite-Gray  Lamp. — 
This  is  a  special  form  of  lamp  designed 
to  be  used  both  as  a  working  and  a  test- 
ing lamp  and  which,  at  one  time,  attained 
a  considerable  popularity  in  this  country. 
It  is  designed  after  the  Gray  lamp,  so 
widely  used  in  England.  As  appears  in 
the  illustration,  Fig.  55,  its  principal 
features  are:  The  hollow  brass  tubes  that 
serve  as  standards  for  the  support  of  the 
cylindrical  brass  bonnet  surrounding  the  gauze  chimney. 
These  standards  are  arranged  to  draw  the  air  from  the  top 
of  the  lamp  when  testing  for  a  thin  stratum  of  air  at  the  roof 
of  a  mine  airway  or  room.  There  are  openings  at  the  bottom 
of  these  hollow  standards  that  can  be  closed  by  sliding  muffs 
when  it  is  desired  to  test  for  gas  Otherwise,  these  openings 
are  exposed  to  the  free  admission  of  the  air  to  the  bottom  of 
the  lamp.  At  thet  op  of  the  lamp,  the  standards  are  affixed 
to  a  brass  plate  to  which  the  bale  or  handle  of  the  lamp  is 


FIG.  55. 


284 


MINE  GASES  AND  VENTILATION 


ALCOHOL 
VESSEL 


attached.  Another  sliding  plate  fits  closely  over  the  first  and 
is  arranged  to  close  the  open  ends  of  the  standards  when  the 
lamp  is  used  as  a  working  lamp. 

The  A.-H.-G.  lamp  is  designed  to  burn  ordinary  sperm, 
cottonseed  or  lard  oil.  The  conical  glass  chimney  has  the 
advantage  of  throwing  the  light  upward  on  the  roof.  The 
illuminating  power  of  the  lamp  is  0.79  cp.  When  tested, 
this  lamp  has  withstood  a  current  velocity  of  6000  ft.  per  min., 

which  is  one  of  the  features  that 
strongly  recommended  its  use  in  this 
country. 

Stokes  Alcohol  Lamp. — This  lamp 
is  designed  by  an  English  mine  in- 
spector, whose  purpose  was  to  supply 
an  alcohol  flame  in  an  oil  burning  lamp, 
the  oil  flame  to  be  used  when  the  miner 
was  working  at  the  face,  and  the 
alcohol  flame  to  be  used  for  testing 
for  gas.  The  lamp  is  an  Ashworth- 
Hepplewhite-Gray  lamp  having  n 
small  vessel  for  holding  the  alcohol 
when  the  lamp  is  to  be  used  for  test- 
ing for  gas.  As  shown  in  the  illustra- 
tion, Fig.  56,  this  alcohol  vessel  is 
screwed  into  the  bottom  of  the  reg- 
ular oil  vessel  of  the  lamp,  its  long 
slim  wick  tube  passing  up  through  a 
hollow  tube  fixed  in  the  oil  vessel  of 
the  lamp.  In  no  other  respect  does 

the  lamp  differ  from  an  A.-H.-G.  lamp.  When  the  Stokes, 
lamp  is  to  be  used  for  testing  for  gas,  the  alcohol  vessel  is 
screwed  in  place  beneath  the  oil  vessel.  The  oil  flame  is  drawn 
down  and  the  lamp  tilted  slightly  to  ignite  the  wick  of  the 
alcohol  lamp,  after  which  the  oil  flame  is  extinguished.  The 
lamp  is  then  ready  for  testing  for  gas. 

The  Clowes  Hydrogen  Lamp. — -This  lamp  is  also  a  modified 
Ash worth-Hepple white-Gray  lamp.  Like  the  Stokes  lamp,  it 
is  provided  with  an  oil  vessel  and  burner  and  a  second  burner 


OIL  VESSEL  with 
ALCOHOL  VESSEL 
inserted  -from  below 

FIG.  56. 


•MINE  LAMPS  AND  LIGHTING 


285 


to   which   hydrogen   gas   is   supplied  from   the   strong   brass 

cylinder  shown  in  the  illustra- 
tion, Fig.  57,  and  which  can  be 

attached  to  or  detached   from 

the  lamp,  as  desired.     There  are 

but  few  of  this  type  of  lamp  in 

the  country  where  it  has  seldom 

been  used,  as  it  is  heavy  and 

cumbersome.       The    hydrogen 

flame,  though  extremely  sensi- 
tive to  gas,  is  easily  extinguished 

when  testing  and  the  use  of  the 

lamp  for  that  purpose  requires 

extreme  care  and  caution.     A 

small  scale  with  crossbars  is  at- 
tached 
to  the 

oil  V6S-   FIG.  57. — Oil  Vessel  and   Hydrogen 
|    .for         Cylinder  Removed  from  Lamp. 

the  purpose  of  observing  and  estimat- 
ing more  accurately  the  height  of  the 
flame  in  testing. 

Hydrogen  gas  is  compressed  to  120 
atmospheres  or  a  pressure  of  1800  Ib. 
per  sq.  in.  at  sea  level.  This  furnishes 
an  ample  supply  for  making  a  large 
number  of  tests  in  the  mine.  The  gas 
cylinder  is  attached  to  the  side  of  the 
oil  vessel  by  a  screw  joint  or  union. 
A  valve  controls  the  flow  of  gas  into 
the  lamp  when  it  is  desired  to  make  a 
test  in  the  mine.  The  oil  flame  is  then 
drawn  down  and  extinguished  after 
the  hydrogen  has  been  turned  on  and 
5g  ignited  in  the  lamp. 

The    Wolf     Lamp. — The    original 

Wolf  lamp  shown  in  the  illustration,  Fig.  58,  is  a  German 
product   that   was   widely  introduced  into  this  country  and 


280 


MINE  GASES  AND  VENTILATION 


FIG.  59. 


MINE  LAMPS  AND  LIGHTING 


287 


PAKT  OF  HISTORICAL  COLLECTION 
howrny  fAKLY  TYPES  OF  SAFETY  LAMPS 


FIG.  60. 


288  MINE  GASES  AND  VENTILATION 

became  very  popular  as  a  working  lamp.  At  the  present 
time,  there  are  a  number  of  lamps  of  this  type  in  use  and 
manufactured  in  this  country,  among  which  may  be  mentioned 
the  Koehler,  the  American  deputy,  the  Hughes  acetylene  lamp, 
and  many  others .  All  of  these,  like  the  Wolf  lamp,  are  designed 
to  burn  a  volatile  oil  contained  in  a  strong  oil  vessel  of  pressed 
steel,  in  which  absorbent  cotton  is  placed  to  retain  the  oil  and 
minimize  the  danger  of  leaking  should  the  lamp  be  overturned. 

The  volatile  oil  flame  is  particularly  sensitive  to  gas,  which 
enables  this  lamp  to  show  gas  when  less  than  1  per  cent,  is 
present  in  the  mine  air.  A  volatile  oil,  however,  cannot  be 
recommended  for  the  purpose  of  testing  for  gas,  owing  to  the 
fuel  cap  that  is  often  mistaken  for  a  gas  cap  when  no  gas  is 
present.  Owing  to  the  ease  with  which  a  volatile  oil  flame  is 
extinguished  in  the  mine,  all  such  lamps  are  provided  with 
igniters.  The  original  Wolf  lamp  is  claimed  to  have  an  il- 
luminating power  of  1.45  cp.,  while  the  average  of  this  type 
of  lamp  will  but  slightly  exceed  a  single  candlepower. 

On  the  two  pages  preceding  will  be  found  most  of  the  impor- 
tant types  of  mine  safety  lamps  grouped  in  a  historical  setting 
that  cannot  fail  to  be  of  interest  in  connection  with  the 
subject.  These  appear  as  Figs.  59  and  60. 

PERMISSIBLE  MINE  SAFETY  LAMPS 

In  "  Schedule  7,  issued  by  the  Federal  Bureau  of  Mines,  the 
engineers  of  the  bureau  have  defined  what  is  to  be  understood 
as  a  " permissible "  miners'  safety  lamp  in  the  following  words: 

Definition. — The  Bureau  of  Mines  considers  a  miners'  safety  lamp  to 
be  permissible  for  use  in  gaseous  mines  if  the  details  of  the  construction  of 
the  lamp  are  the  same  as  those  of  the  type  of  lamp  that  has  passed  the 
tests  made  by  the  bureau  and  hereinafter  described. 

Conditions  of  Testing. — The  conditions  under  which  the  Bureau  of 
Mines  will  examine,  inspect,  and  conduct  tests  on  miners'  safety  lamps 
are  as  follows: 

1.  The  examination,  inspection  and  tests  will  be  made  at  the  experi- 
ment station  of  the  Bureau  of  Mines,  at  Pittsburgh,  Pa. 

2.  Applications,  for  inspection,  examination  and  test  shall  be  made  to 
the  Director,  Bureau  of  Mines,  Washington,  D.  C.,  and  shall  be  accom- 
panied by  a  complete  description  of  the  lamp  and  a  set  of  drawings 
showing  all  the  details  of  the  lamp's  construction. 


MINE  LAMPS  AND  LIGHTING  289 

3.  The  applicant  for  the  inspection,   examination   and  test  will  be 
required  to  furnish  two  lamps  of  each  type,  which  shall  be  sent  prepaid 
to  the  Engineer  in  Charge  of  Lamp  Testing,  Bureau  of  Mines,  Fortieth 
and  Butler  Streets,  Pittsburgh,  Pa.,  and  will  be  retained  by  the  bureau 
as  a  laboratory  exhibit. 

Each  lamp  shall  have  marked  on  it  in  a  distinct  manner  the  name 
of  the  manufacturer  and  the  name,  letter  or  number  by  which  the 
type  is  designated  for  trade  purposes,  and  a  statement  shall  be  made 
whether  or  not  the  lamp  is  ready  to  be  marketed;  also  a  statement 
describing  the  fuel  used,  its  trade  name  and  properties.  The  appli- 
cant may  supply  t  he  fuel  for  the  test  if  he  so  desires. 

4.  Upon  the  receipt  of  a  lamp  for  which  application  has  been  made 
for  examination,   inspection   or  test,   the  engineer  in   charge   of  lamp 
testing  will  advise  the   applicant  whether  additional  spare  parts  are 
deemed  necessary  to  facilitate  a  proper  test  of  the  lamp,  and  the  appli- 
cant will  be  required  to  furnish  such  parts  as  may  be  requested. 

5.  No  lamp  will  be  tested  unless  the  type  submitted  is  in  the  com- 
pleted form  in  which  it  is  to  be  placed  on  the  market. 

6.  Only  the  engineer  in  charge  of  lamp  testing,  his  assistants  and 
one  representative  of  the  applicant  will  be  permitted  to  be  present  during 
the  conduct*  of  the  tests. 

7.  The  conduct  of  the  tests  shall  be  entirely  under  the  direction  of 
the  bureau's  engineer  in   charge  of  the  investigation.     The  tests  will 
be  made  in  accordance  with  a  predetermined  schedule,  which  is  outlined 
herein. 

8.  As  soon   as  possible  after  the  receipt  of  the  formal  application 
for  test,  the  applicant  will  be  notified  of  the  date  on  which  his  lamp 
will  be  tested  and  the  amount  and  character  of  additional  material  it 
will  be  necessary  for  him  to  submit. 

9.  The  tests  will  be  made  in  the  order  of  the  receipt  of  applications 
for   test,   provided  the   necessary  lamps   and   material   are   submitted 
at  the  proper  time. 

10.  The  details  of  the  results  of  the  tests  shall  be  regarded  as  confiden- 
tial by  all  present  at  the  tests  and  shall  not  be  made  public  in  any  way 
prior  to  their  official  announcement  by  the  Bureau  of  Mines. 

11.  The  results  of  tests  made  on  lamps  that  fail  to  pass  the  require- 
ments shall  not  be  made  public  but  shall  be  kept  confidential,  except 
that  the  person  submitting  the  lamp  will  be  informed  with  a  view  of 
possible  remedy  of  defects  in  future  lamps  submitted;  but  such  changes 
other  than  changing  the  glass  globe  or  chimney,  will  not  be  permitted 
while  the  testing  is  in  progress. 

12.  Tests  will  be   made   for  manufacturers,   manufacturers'    agents, 
state  mine  inspectors  and  mine  operators. 

13.  A  list  of  permissible  lamps  and  the  results  of  their  tests  will 
be  made  public,  from  time  to  time,  by  the  Bureau  of  Mines. 

14.  The  glass  globe  or  chimney  shall  be  marked  in  a  distinct  manner 
by  a  name  or  design  by  which  its  type  is  designated  for  trade  purposes. 


290  MINE  GASES  AND  VENTILATION 

Mechanical  Tests. — The  following  mechanical  tests  will  be 
applied  to  every  lamp  submitted  to  the  bureau  to  ascertain  its 
strength  and  resistance  under  the  rough  usage  common  to 
mining  work. 

1.  The    lamp    is    dropped,  by  means  of  a  mechanical  arrangement, 
onto  a  wooden  floor,  from  a  height  of  6  ft.  measured  from  the  floor  to  the 
bottom  of  the  lamp,  which  has  been  fitted  together  complete  with  the 
glass,  a  component,  part  of  the  lamp. 

Five  successive  trials  are  made,  the  lamp  being  fitted  with  a  dif- 
ferent glass  each  time.  The  lamp  passes  the  test  if  the  glass  is  broken 
in  not  more  than  one  of  the  five  trials.  Should  the  glass  be  broken 
in  two  but  not  more  than  two  of  the  five  trials,  the  lamp  is  submitted 
to  five  more  trials  with  fresh  glasses  and  if  the  glass  breaks  in  two  of  them 
the  lamp  will  be  considered  as  having  failed  to  pass  the  test. 

2.  A  weight  of  5  Ib.  is  dropped,  from  a  height  of  6  ft.,  onto  the  lamp 
standing  vertically  on  a  wooden  platform  beneath  the  weight,. 

The  height  of  6  ft.  is  measured  between  the  bottom  of  the  weight  and 
the  top  of  the  lamp.  The  weight  is  a  lead  disk  3  in.  in  diameter  and  1% 
in.  thick  and  is  dropped  mechanically. 

Should  the  glass  of  the  lamp  break,  two  more  trials  are  made,  each 
with  a  different  glass,  and  if  the  glass  breaks  in  either  the  second  or 
third  trial  the  lamp  will  be  considered  as  having  failed  to  pass  the  test. 

3.  A  weight  of  10  Ib.,  attached  to  a  cord  the  other  end  of  which  is 
secured  to  the  bottom  of  the  lamp,  is  dropped  a  distance  of  6  ft.,  the  lamp 
being  suspended  at  a  height  of  7  ft.,  from  the  ground. 

The  lamp  is  gripped  by  means  of  claws,  or  slung  by  means  of  straps 
fastened  around  its  upper  part,  above  the  standards  protecting  the 
glass.  A  plate  is  fastened  to  the  bottom  of  the  lamp  and  the  cord  is 
attached  to  the  center  of  this  plate.  The  weight  is  a  lead  disk  4% 
in.  in  diameter  and  l^  in.  thick.  It  is  dropped  mechanically. 

This  test  is  repeated  three  times.  If,  as  the  result  of  any  one  of 
these  three  trials,  the  security  of  the  lamp  is  found  to  be  defective  in 
any  way  the  lamp  will  be  considered  as  having  failed  to  pass  the  test. 

Tests  1,  2,  and  3  are  to  be  made  in  succession  on  one  lamp.  Crack- 
ing of  the  glass  will  be  regarded  as  a  breakage. 

Photometric  Test. — The  lamp  is  required  to  give  a  minimum  candle- 
power  of  0.30,  as  compared  with  a  pentane  standard,  during  a  period  of 
10  hours. 

Explosion  Test. — After  a  lamp  has  passed  the  mechanical  tests,  it  will 
be  tested  by  placing  the  lighted  lamp  in  an  explosive  mixture  of  gas  and 
air,  as  follows: 

1.  In  currents  of  air  and  gas  containing  8%  per  cent,  of  natural  gas 
drawn  from  the  Pittsburgh  gas  mains.  In  a  gallery  (lamp  gallery 
No.  1)  a  lamp  which  has  passed  the  mechanical  tests  is  tested,  with  a 


MINE  LAMPS  AND  LIGHTING  291 

fresh  glass  if  necessary,  in  horizontal,  inclined  and  vertical  currents 
of  the  explosive  mixture  of  gas  and  air: 

a.  In  a  horizontal  current,  velocity  600  to  2500  ft.  per  min. 

b.  In  a  45  deg.  descending  current,  velocity  600  to  2500  ft.  per  min. 

c.  In  a  45  deg.  ascending  current,  velocity  600  to  2500  ffc.  per  min. 

d.  In  a  vertical  descending  current,  velocity  600  to  2500  ft.  per  min. 

e.  In  a  vertical  ascending  current,  velocity  600  to  2500  ft.  per  min. 
Trials  will  be  made  at  velocities  of  600,  800,  1000,  1200,  1500,  2000, 

and  2500  ft.  per  min.  Into  the  horizontal  current  moving  at  1500  ft. 
per  min.,  the  lamp  will  be  suddenly  thrust  from  below. 

The  duration  of  each  trial  is  two  minutes  and  each  trial  is  repeated 
three  times.  An  ignition  exterior  to  the  lamp  will  cause  the  lamp 
to  be  rejected. 

2.  In  a  still  atmosphere  (lamp  gallery  No.  3)  containing  8>£  per  cent, 
of  natural  gas.  The  lamp  is  placed,  with  a  fresh  glass  if  necessary, 
in  this  inflammable  atmosphere  for  three  minutes.  Five  separate 
determinations  will  be  made.  An  ignition  exterior  to  the  lamp  will 
cause  the  lamp  to  be  rejected. 

Tests  of  Glasses. — 1.  A  weight  of  1  ,lb.  is  dropped  by  means  of  a 
mechanical  arrangement,  from  a  height  of  4  ft.,  upon  the  glass  placed  in  a 
vertical  position  on  a  wooden  floor.  The  weight  is  a  lead  disk  2^  in.  in 
diameter  ^  in.  thick.  Twenty  glasses  of  any  one  kind  will  be  tested. 
Two  failures  in  the  twenty  will  cause  the  glasses  to  be  rejected. 

2.  Ten  glasses  are  heated  in  an  air  balh  to  a  temperature  of  212  deg.  F. 
and  when  at  that  temperature  are  removed  from  the  bath  and  plunged 
into  water  at  a  temperature  of  60  deg.  to  65  deg.  F.  One  failure  in 
ten  will  cause  the  glasses  to  be.  rejected. 

If  the  lamp  has  two  glasses  the  outer  glass  will  be  tested  by  mechan- 
ical means  only  and  the  inner  glass  by  heating  onlv. 

Igniter  Tests. — Lamps  having  internal  igniters  will  be  tested  to  deter- 
mine the  safety  and  permissibility  of  the  ignifcer  device:  The  permissi- 
bility of  the  lamp  will  be  dependent  in  part  on  the  result  of  the  teste  of  the 
igniter  device. 

These  tests  will  be  made  to  determine  the  liability  of  external  ignition 
when  the  igniter  device  is  operated  in  the  presence  of  inflammable  mix- 
tures of  gas  and  air  under  such  conditions  as  may  be  determined  by  the 
engineer  in  charge  of  lamp  testing,  for  each  type  of  igniting  device. 
Tests  will  be  made  to  determine : 

1.  If  external  ignition   is  possible   when  the  igniter  is  operated   in 
still  and  moving  currents  of  gas  and  air  mixtures. 

2.  To  determine  if  the  residue  left  in  the  lamp  after  working  the 
igniter  device  is  a  source  of  danger  in  subsequent  use  of  the  lamp  in 
inflammable  mixtures  of  gas  and  air. 

3.  To  determine  the  nature  of  the  material  used  in  -the  igniter  device. 
The  igniter  will  have  passed  the  tests  if  no  external  ignition  is  caused 

by  manipulating  the  igniter  when  in  position  within  a  double-gauze 


292  MINE  GASES  AND  VENTILATION 

safety  lamp,  or  if  no  external  ignition  is  caused  by  the  use  of  the  lamp 
in  inflammable  mixtures  of  gas  and  air  after  the  igniter  has  been  in 
service. 

Applicants  for  tests  will  be  required  to  furnish  two  complete  igniter 
devices  and  5  dozen  igniter  refills,  which  shall  be  shipped  in  sealed 
boxes  or  packages  with  the  trade  name  written  on  the  outside  and 
addressed  to  the  Engineer  in  Charge  of  Lamp  Testing,  Bureau  of  Mines, 
Pittsburgh,  Pa.  When  known  by  the  applicant,  the  proximate  chemical 
composition  of  the  igniter  tape  or  point  should  be  furnished  and  the 
place  of  its  manufacture. 

Note. — The  inflammable  gas  used  in  these  series  of  tests  will  be  the 
natural  gas  supplied  to  the  city  of  Pittsburgh  The  composition  of  this 
gas  is  approximately:  Methane,  83.1  per  cent. ;  ethane,  16  per  cent. ;  nitro- 
gen, 0.9  per  cent. ;  carbon  dioxide,  a  trace. 

Lamps  in  the  course  of  development  may  be  submitted  by  manu- 
facturers for  inspection  and  preliminary  tests,  with  a  view  to  ascer- 
taining defective  construction  or  the  misapplication  of  safety  principles. 
The  nature  of  such  inspection  and  tests  will  be  determined  by  the 
engineer  in  charge  of  lamp  testing. 

Approval  of  Safety  Lamps. — The  manufacturers  of  such  types  of  lamps 
as  have  passed  the  tests  of  the  bureau  may  attach  a  plate  containing,  or 
stamp  into  the  metal  of  the  lamp,  the  following  inscription: 

PERMISSIBLE    MINERS*    SAFETY  LAMP. 
U.    S.    BUREAU    OF    MINES    APPROVAL    NO. . 

Before  claiming  the  bureau's  approval  of  any  modification  of  any 
approved  type  of  lamp,  the  manufacturer  shall  submit  to  the  bureau 
drawings  that  show  the  extent  and  nature  of  such  modifications.  Each 
approval  of  a  permissible  lamp  will  be  given  a  serial  number,  and  ap- 
provals of  modified  types  will  bear  the  same  serial  number  as  the  original, 
with  the  addition  of  the  letters  a,  b,  c,  etc. 

The  bureau  will,  on  application,  make  separate  tests  of  glasses  manu- 
factured for  use  in  connection  with  any  lamp  that  has  been  approved 
by  the  bureau  under  the  provisions  of  this  schedule.  Glass  globes  that 
fulfill  the  requirements  of  the  tests  will  be  approved  for  types  manu- 
factured in  every  particular  like  those  submitted  that  passed  the  test. 

The  bureau  will,  on  application,  make  separate  tests  of  internal 
igniter  devices  for  use  with  any  type  of  lamp  that  has  been  approved 
by  the  bureau  under  the  provisions  of  this  schedule.  Igniters  that 
fulfill  the  requirements  of  the  tests  will  be  approved  for  types  manu- 
factured in  every  particular  like  those  submitted  that  passed  the  tesl . 

The  bureau's  approval  of  any  lamp  shall  be  construed  as  applying 
to  all  lamps  of  the  same  type  as  tested,  made  by  the  same  manufacturer 
and  having  the  same  construction  in  detail,  but  to  no  other  lamp.  The 


MINE  LAMP 8  AND  LIGHTING  293 

bureau  reserves  the  right  to  rescind,  for  cause,  at  any  time,  any  ap- 
proval granted  under  the  conditions  herein  set  forth. 

Notification  to  Manufacturer. — As  soon  as  the  bureau's  engineers  are 
satisfied  that  a  lamp  is  permissible  the  manufacturer,  agent  or  applicant 
and  the  mine  inspection  departments  of  the  several  states  shall  be  notified 
to  that  effect.  As  soon  as  a  manufacturer  receives  formal  notification 
that  his  lamp  has  passed  the  tests  prescribed  by  the  Bureau  of  Mines,  he 
shall  be  free  to  advertise  such  lamp  as  permissible. 

Fees  for  Testing. — Careful  investigation  has  been  made  regarding  the 
necessary  expenses  involved  in  testing  miners'  safety  lamps  at  the  Pitts- 
burgh experiment  station,  and  the  following  schedule  of  feesto  be  charged 
on  and  after  February  15,  1915,  has  been  established  and  approved  by 
the  Secretary  of  the  Interior,  in  accordance  with  the  provisions  of  the 
statute  previously  quoted: 

Preliminary  inspection  and  test $10. 00 

Complete  lamp  test 50 . 00 

Candlepower   test 5 . 00 

Separate  glass  globe  tests 5 . 00 

'  Separate  igniter  tests 10 . 00 

The  fees  specified  above  may  be  increased  to  cover  the  cost  of  test- 
ing an  unusually  complicated  type  of  lamp,  .and  are  also  subject  to 
change  upon  the  recommendation  of  the  Director  of  the  Bureau  of 
Mines  and  the  approval  of  the  Secretary  of  the  Interior. 

USE  AND  CARE  OF  SAFETY  LAMPS 

No  safety  lamp,  however  perfect,  is  safe  when  improperly 
used;  nor  has  the  safety  lamp  yet  been  devised  that  is  fool- 
proof. For  these  reasons,  a  safety  lamp  should  never  be  en- 
trusted to  an  incompetent  or  an  unreliable  person.  With  the 
single  exception  of  the  lamps  used  by  the  mine  examiners  or 
firebosses,  all  lamps  used  in  a  mine  should  be  the  property  and 
care  of  the  operator. 

The  Lamphouse  or  Station. — A  lamphouse  or  lampstation 
should  be  established  convenient  to  the  mine  entrance,  where 
the  miners  can  secure  their  lamps  when  entering  the  mine 
and  return  the  same  on  coming  to  the  surface.  Each  lamp 
should  be  stamped  with  a  number  and,  as  far  as  practicable, 
the  same  lamp  should  be  given  to  the  same  man,  each  day,  and 
he  be  made  responsible  for  its  use  and  condition. 

The  lamphouse  should  be  in  charge  of  a  competent  man  and 
one  or  more  assistants,  whose  duties  would  be  to  receive  and 


204  MINE  GASES  AND  VENTILATION 

deliver  all  lamps  in  return  for  checks  bearing  the  lamp  number. 
No  lamp  must  be  given  out,  except  in  return  for  this  check, 
which  should  be  placed  in  the  pigeonhole  from  which  the 
lamp  is  taken  or  hung  on  its  hook  ready  to  be  given  back  to  the 
man  when  his  lamp  is  returned  at  the  close  of  the  shift. 

A  properly  organized  and  arranged  lamphouse  will  have  one 
or  more  lampracks  with  holes  or  .hooks  for  the  lamps.  Each 
hole  or  hook  has  a  number  corresponding  to  that  on  the  lamp. 
Tables  are  provided  where  the  lamps  can  be  taken  apart, 
cleaned,  filled  and  trimmed,  after  which  they  are  carefully 
assembled,  inspected  and  returned  to  their  respective  places 
in  the  rack. 

The  oil  for  filling  the  lamps  should  be  drawn  from  a  tank  or 
reservoir  outside  of  the  building.  No  oil  container  other  than 
the  lamp  vessels  should  be  permitted  in  the  lamphouse  or  sta- 
tion, which  should  be  of  fireproof  construction  and  kept  free 
from  all  accumulations  of  oily  waste  or  other  material  liable 
to  spontaneous  combustion.  The  presence  of  a  man's  lamp  or 
check  on  the  lamprack  will  indicate  whether  he  has  come  out  or 
is  still  in  the  mine  and  will  thus  serve  the  same  purpose  as  a 
checking  board,  in  that  respect. 

No  one  must  be  permitted  in  the  lamphouse  other  than  those 
in  charge.  All  lamps  should  be  delivered  through  one  or  more 
windows  opening  on  a  passageway.  The  work  of  delivering 
and  receiving  lamps,  where  a  large  number  of  men  are  em- 
ployed, will  be  greatly  expedited  if  there  are  several  windows, 
each  corresponding  to  a  division  in  the  numbering  of  the  lamps. 
A  further  advantage  in  such  an  arrangement  is  that  each  divi- 
sion can  be  in  charge  of  a  man  who  is  responsible  for  the  lamps 
in  that  division. 

Handling  of  Safety  Lamps. — A  safety  lamp  must  never  be 
given  to  a  man  who  has  not  been  instructed  and  drilled  in  re- 
spect to  its  use.  Before  being  entrusted  with  a  safety  lamp, 
a  man  must  show  his  ability  to  determine  the  presence  of  gas, 
by  observing  the  flame  cap  formed  in  his  lamp.  He  should  be 
taught  how  to  proceed  when  he  has  observed  a  cap  in  his  lamp, 
and  cautioned  to  carefully  lower  his  lamp  and  withdraw  quietly 
but  promptly  from  the  place. 


MINE  LAMPS  AND  LIGHTING  295 

• 

The  man  should  be  shown  how  his  lamp  may  flame  should 
a  larger  proportion  of  gas  be  present  in  the  air.  He  should  be 
instructed,  in  that  case,  as  to  the  necessity  of  maintaining  his 
presence  of  mind  and  making  no  quick  movement  with  the 
lamp,  which  must  be  withdrawn  promptly  but  cautiously  from 
the  gas,  by  lowering  the  lamp  toward  the  floor.  The  man 
should  be  further  cautioned  in  regard  to  the  danger  of  dis- 
turbing a  body  of  gas,  which  may  then  surround  him  and  make 
it  difficult  for  him  to  escape  with  safety. 

A  safety  lamp  must  always  be  held  in  an  upright  position 
and  protected  against  a  rush  of  air  such  as  follows  a  blast  in 
the  mine.  It  is  necessary  to  protect  the  lamp  when  walking 
against  a  strong  air  current.  A  lamp  should  never  be  swung, 
but  should  be  held  quietly  at  one's  side  when  going  from  place 
to  place  in  the  mine.  Care  must  be  taken  not  to  drop  the 
lamp  or  permit  it  to  fall.  Under  no  circumstances  must  a  man 
tamper  with  his  lamp  or  attempt  any  experiment.  If  the 
lamp  is  accidentally  extinguished,  the  man's  duty  is  to  proceed 
at  once  to  the  nearest  relighting  station,  which  should  be  pro- 
vided at  a  convenient  point  in  the  mine. 

TESTING  FOR  GAS  BY  INDICATORS 

The  work  of  testing  for  gas  is  the  most  important  work  to 
be  performed  in  the  operation  of  a  gaseous  mine  and  can  only 
be  safely  entrusted  to  a  mine  examiner,  fireboss  or  deputy  who 
has  had  experience  both  in  the  testing  and  the  handling  of  gas. 
The  examination  of  a  mjne  for  gas  and  other  dangers  must  be 
performed  conscientiously  and  faithfully.  The  work  will  not 
permit  of  the  taking  of  chances,  as  the  life  of  every  worker  in 
the  mine  depends  on  the  thoroughness  and  capability  of  the 
examiner. 

From  time  to  time,  different  means  have  been  employed  in 
making  the  test  for  gas  in  mine  workings.  These  consist  in 
various  forms  of  indicators  and  detectors  especially  designed 
to  reveal  the  presence  of  gas  in  mine  air  and  ascertain  its  per- 
centage. Besides  these  appliances,  a  few  of  which  will  be 
described  briefly,  there  is  the  old-established  flame  test,  made 
by  the  use  of  the  Davy  or  other  safety  lamp,  and  which  is 


296  MINE  GASES  AND  VENTILATION 

• 

still  the  most  largely  employed  by  mine  examiners  and  fire- 
bosses. 

Numerous  Gas  Indicators.— Perhaps  the  earliest  attempt  to 
devise  a  means  of  indicating  the  percentage  of  gas  present  in 
air  consisted  of  a  glass  tube  into  which  had  been  fused  a 
platinum  wire  that  could  be  rendered  incandescent  by  an 
electric  current.  A  sample  of  the  air  to  be  tested  was  drawn 
into  the  tube  where  the  gas  contained  in  the  air  was  consumed 
by  the  incandescent  wire.  The  volume  of  the  remaining  gases 
was  then  measured.  Comparing  this  with  the  original  volume 
of  gas  and  air  gave  the  percentage  of  gas  present  in  the  air. 
Devices  of  this  nature,  however,  were  never  of  practical  value, 
until  the  recent  design  of  such  a  gas  detector  by  George  A. 
Burrell,  of  the  Federal  Bureau  of  Mines,  which  will  be  described 
later  (see  p.  299). 

Another  device  depended  on  the  increase  of  pressure  in  an 
air  container  that  was  separated  from  a  similar  container  of 
gas  and  air  by  a  porous  partition  through  which  diffusion  of 
the  gas  into  the  air  took  place.  The  resulting  increase  of 
pressure  in  the  first  container  was  an  index  of  the  percentage 
of  gas  present  in  the  sample  tested,  but  the  device  had  no 
practical  value  for  use  in  mines.  Still  another  device  depended 
on  the  rise  in  temperature  caused  by  the  absorption  of  gas  by 
platinum  black,  which  coated  the  bulb  of  one  of  two  ther- 
mometers. The  rise  in  temperature  thus  indicated  furnished 
the  means  of  determining  approximately  the  percentage  of 
gas  present.  Again,  another  device  depended  on  the  com- 
pression of  a  sample  of  gas-charged  air  contained  in  a  strong 
glass  tube  into  which  was  fitted  a  piston.  The  rapid  compres- 
sion of  the  air  in  the  tube  would  ignite  the  gas  and  cause  a 
flash  when  not  less  than  5  per  cent,  of  gas  was  present. 

The  Liveing  indicator  was  a  more  accurate  means  of  deter- 
mining percentages  of  gas,  but  this  also  never  came  largely 
into  use.  Two  platinum  wires  of  equal  resistance  were  ren- 
dered incandescent  by  an  electric  current.  One  of  these  wires 
was  inclosed  in  a  tube  containing  a  sample  of  the  air  to  be 
tested,  while  the  other  wire  was  in  pure  air.  An  ingenious 
sliding  arrangement  of  the  two  tubes  containing  the  wires 


MINE  LAMPS  AND  LIGHTING  297 

provided  a  means  of  comparing  their  relative  brilliancy,  which 
furnished  a  suggestion  of  the  percentage  of  gas  present  in  the 
air  tested.  None  of  these  devices,  however,  can  be  considered 
of  any.  practical  importance  in  coal  mining. 

The  Shaw  Gas  Machine. — This  machine,  though  not  of 
portable  form,  on  which  account  it  could  not  be  tak^n  into 
the  mine  but  samples  of  air  to  be  tested  must  be  brought  to  the 
surface,  furnished  a  means  of  correctly  determining  the  ex- 
plosibility  of  samples  of  air  collected  in  the  mine  workings. 
For  this  purpose,  it  was  formerly  used  at  many  large  collieries. 
The  disadvantage  in  its  use  lay  in  the  fact  that  a  test  could 
not  be  made  on  the  spot  and  time  must  elapse  between  the 
taking  of  the  sample  of  air  and  knowing  the  results  of  the  test. 
In  that  time,  conditions  in  the  mine  might  materially  change, 
which  rendered  the  test  valueless  for  the  purpose  intended. 

The  Shaw  machine  consists  of  two  cylinders  whose  volume 
ratio  is  known.  Both  cylinders  are  fitted  with  air-tight  pis- 
tons operated  by  a  single  lever  arm.  By  this  means  exact 
proportions  of  gas  and  air  can  be  pumped  into  a  combustion 
chamber  where  they  are  ignited  when  the  mixture  becomes 
explosive.  A  graduated  scale  indicates  the  volume  percentage 
of  air  and  gas  present  when  explosion  occurs. 

In  the  operation  of  this  machine,  it  is  first  necessary  to 
standardize  an  artificial  gas  supply  to  ascertain  the  lower  ex- 
plosive limit  of  the  gas.  To  do  this  the  machine  was  arranged 
so  that  the  larger  cylinder  would  pump  pure  air  while  the 
smaller  one  pumped  gas,  and  the  point  noted  when  explosion 
occurred.  This  having  been  done,  the  tube  that  formerly 
supplied  pure  air  to  the  larger  cylinder  is  now  connected  with 
the  bag  containing  the  sample  of  mine  air  to  be  tested,  while 
the  smaller  cylinder  continues  to  pump  its  proportion  of  the 
standard  gas.  Evidently,  a  less  ratio  of  the  supply  from  the 
two  cylinders  will  now  be  required  to  produce  an  explosion, 
should  the  air  pumped  by  the  larger  cylinder  contairi  some  gas. 
The  difference  shown  on  the  graduated  scale  gives  the  percen- 
tage of  gas  present  in  the  air  tested. 

The  Beard-Mackie  Sight  Indicator. — This  is  a  simple  and 
extremely  practical  device  designed  to  be  attached  to  the 


298 


MINE  GASES  AND  VENTILATION 


burner  of  a  safety  lamp  burning  sperm,  cottonseed  or  lard  oil 
but*  not  a  voltaile  oil.  As  shown  on  the  right,  in  the  illus- 
tration, Fig.  61,  the  device  consists  of  a  U-shaped  support 
mounted  on  a  small  brass  disk  that  fits  over  the  burner  and 
is  held  in  place  by  the  screw  nipple  of  the  lamp.  On  this  sup- 
port are  arranged  fine  platinum  wires  at  fixed  heights  above  the 
lamp  flame. 

The  lower  straight  standard  wire  is  for  the  purpose  of  stand- 
ardizing the  flame,  which 
is  raised  to  a  height  just 
sufficient  to  incandesce 
that  wire.  This  must 
be  done  in  pure  air,  al- 
though a  slight  altera- 
tion in  the  height  of  the 
flame  produces  no  prac- 
tical effect  in  determin- 
ing the  percentage  of  gas 
by  the  incandescence  of 
the  successive  percent- 
age wires  when  the  lamp 
is  taken  into  the  mine. 
Indeed,  the  standardiz- 
ing of  the  flame  is  gener- 
ally done  after  entering 
the  mine  when  the  ex- 
aminer has  once  become 
FlG  61  acquainted  with  the  use 

of  this  indicator. 

The  percentage  wires  are  each  looped  at  the  center,  the 
purpose  being  to  make  their  incandescence  more  perceptible 
when  observed  through  the  gauze  of  the  Davy  lamp,  as  shown 
on  the  left  of  the  figure.  The  incandescence  mounts  higher 
in  the  percentage  wires  as  the  proportion  of  gas  in  the  mine  air 
increases  and  the  uppermost  wire  incandesced  determines  the 
percentage  of  explosibility  of  the  mine  air. 

The  use  of  the  sight  indicator  furnishes  the  means  of  deter- 
mining with  considerable  ~  accuracy  the  explosibility  of  mine 


DAVY  LAMP 

WITH 
SIGHT  INDICATOR 


BEARD-MACKIE 
S/GHT  INDICATOR 
FOR  DETECT/NQ  GAS 


MINE  LAMPS  AND  LIGHTING 


299 


air,  at  the  point  and  at  the  moment  the  test  is  made.  Its 
use  eliminates  the  necessity  of  the  fireboss  guessing  the  per- 
centage from  the  height  of  the  flame  cap  observed  in  his  lamp. 
It  enables  a  just  comparison  to  be  made  between  the  reports  of 
different  firebosses  whose  judgment  may  differ,  or  who  may 
not  be  equally  capable  of  discerning  the  caps  formed  in  their 
lamps. 

With  proper  care,  the  sight  indicator  can  be  used,  for  a  year 
or  more,  by  a  fireboss  when  making 
his  morning  examination  of  the  mine. 
Its  construction  is  naturally  some- 
what delicate,  which  requires  it  to  be 
carefully  handled  when  being  inserted 
or  taken  out  of  the  lamp.  A  careless 
fireboss  will  often  permit  his  lamp  to 
smoke  and  carbonize  the  wires,  which 
interferes  with  their  delicacy.  The 
same  effect  is  caused  by  burning  a 
poor  quality  of  oil  or  oil  mixed  with 
kerosene,  which  increases  the  smoki- 
ness  of  the  flame. 

The  advantages  derived  by  the  use 
of  the  indicator  are  that  it  standard- 
izes all  tests  for  gas,  making  them 
comparable.  It  eliminates  the  guess- 
ing of  the  height  of  a  flame  cap  and 
the  percentage  of  gas  indicated  there- 
by. It  indicates  the  presence  of  gas 
as  low  as  one-half  of  1  per  cent.  The 
indications  are  plainly  visible  by  the  incandescence  of  the 
looped  wires.  The  presence  of  an  indicator  in  a  lamp  has 
often  avoided  the  extinction  of  the  lamp  in  gas  and  reduces 
the  tendency  to  internal  explosion  in  the  lamp.  Finally,  all 
indications  are  made  with  a  normal  flame,  which  not  only 
saves  time  but  avoids  the  necessity  of  lowering  the  flame  and 
possibly  extinguishing  it  when  making  a  test. 

The  Burrell  Gas  Detector. — This  -device,  which  is  shown  in 
section  in  the  illustration,  Fig.  62,  consists  of  a  brass  tube  A 


FIG.  02. 


300  MINE  GASES  AND  VENTILATION 

surmounted  by  a  screw  cap  P  equipped  with  a  valve  V,  a 
little  cup  K  and  two  binding  posts  M  and  N.  Connected 
with  and  supported  by  the  latter  is  a  fine  platinum-wire  bridge 
F,  which  can  be  rendered  incandescent  by  the  current  from  an 
electric  battery.  A  stout  gage-glass  C  is  surmounted  by  a 
brass  reservoir  or  cap  H  to  which  a  rubber  tube  R  is  attached. 
Both  the  gage-glass  C  and  the  brass  tube  A  are  set  into  an 
aluminum  base  X,  by  which  they  are  connected,  forming  a 
U-tube  after  the  manner  of  a  water  gage.  A  graduated  scale 
0  provides  the  means  of  measuring  the  height  of  water  column 
in  the  gage-glass. 

In  the  use  of  this  instrument  for  the  detection  of  mine  gas  in 
the  workings,  the  brass  cap  P  is  unscrewed  and  water  poured 
into  A,  until  it  rises  in  the  gage-glass  to  a  level  indicated  by  the 
zero  of  the  scale  at  S.  This  level  corresponds  to  the  level  Q 
in  the  brass  tube  A,  just  below  the  platinum  wire  F. 

When  a  test  is  to  be  made  in  the  mine  the  valve  V  is  first 
opened  and  the  operator  blows  gently  into  the  rubber  tube  R, 
depressing  the  water  level  in  the  gage-glass  and  causing  it  to 
rise  in  the  brass  tube,  until  it  appears  in  the  little  cup  K, 
or  until  a  slight  click  of  the  valve  V  tells  that  the  water  has 
completely  filled  the  combustion  space  Y,  in  the  top  of  the 
brass  tube.  The  rubber  tube  attached  at  R  is  now  pinched 
with  the  fingers  and  the  instrument  raised  to  the  roof  or  into 
the  cavity  where  it  is  desired  to  test  the  air  for  gas.  In  that 
position,  the  rubber  tube  is  released  and  the  water  level  at 
once  falls  in  A  and  rises  iri  C  to  where  it  originally  stood 
at  zero  of  the  scale.  By  this  action,  the  air  to  be  tested  is 
drawn  in  through  the  open  valve  V  and  fills  the  combustion 
space  Y  above  the  water  level  Q. 

When  equilibrium  is  established,  the  valve  V  is  closed  and 
the  battery  current  switched  on,  causing  the  incandescence  of 
the  wire  bridge  F,  which  is  plainly  observed  through  the 
small  glass  window  E.  About  1 J^  min.  is  required  to  consume 
all  the  gas  present  in  the  air  contained  in  the  combustion  space 
above  the  water.  The  current  is  now  turned  off  and  the  in- 
strument shaken,  for  the  purpose  of  cooling  the  air  and  gaseous 
products  of  the  combustion,  and  permit  of  their  volume  being 


MINE  LAMPS  AND  LIGHTING  301 

measured  at  the  original  temperature.  As  cooling  takes  place, 
the  water  rises  in  A  arid  falls  in  the  gage-glass,  until  it  becomes 
stationary  at  a  certain  level.  The  graduation  at  that  point 
will  show  the  percentage  of  gas  that  was  present  in  the  air 
tested.  The  aluminum  scale  0  is  easily  removable  and  is 
graduated  for  the  detection  of  any  combustible  gas  or  vapor. 
The  two  scales  that  appear  in  the  figure  are  for  hydrogen  (H) 
and  carbon  monoxide  (CO). 

This  instrument  has  proved  quite  effective  for  the  purpose 
intended  in  its  design.  There  is  no  doubt  but  that  some  of  the 
carbon  dioxide  produced  by  the  combustion  of  the  gas  is 
absorbed  in  the  water  when  the  instrument  is  shaken;  but  this 
is  probably  largely  compensated  by  the  slightly  higher  water 
level  in  A  above  that  in  the  gage-glass  C,  at  the  time  the  mea- 
surement is  taken.  This  difference  of  level  is,  moreover,  ren- 
dered extremely  slight  by  reason  of  the  relatively  larger  diameter 
of  the  tube  A,  as  compared  with  the  bore  of  the  gage-glass  C. 
Actual  tests  of  the  results  obtained  in  the  mine,  by  comparison 
with  the  analysis  of  the  same  air,  in  the  laboratory,  show  the 
following  percentages  which  are  not  exceptional. 


By  detector  
By  analysis  

0.4 
0.45 

0.7 
0.57 

0.9 
1.11 

1.6 
1.61 

1.9 
1.23 

1.5 
1.93 

2.5 
2.52 

2.0 
1.46 

2.2 
2.54 

For  all  practical  purposes,  the  slight  differences  shown  by 
these  figures  between  the  tests  made  in  the  mine  and  the 
analyses  made  in  the  laboratory  are  immaterial. 

THE  FLAME  TEST 

From  the  earliest  time,  the  most  universal  method  of  testing 
for  gas  in  mines  has  been  that  of  observing  the  effect  of  the 
gas  on  the  flame  of  a  safety  lamp.  As  is  well  known,  in  every 
candle,  or  lamp  flame  burning  oil,  there  are  three  zones  as 
indicated  in  the  illustration,  Fig.  63.  The  inner  zone  A  is 
dark,  being  filled  with  the  hydrocarbon  vapors  formed  by  the" 
vaporization  of  the  oil.  There  is  no  combustion  taking  place 
in  this  zone.  The  heat  of  the  flame  dissociates  the  hydrogen 
and  carbon  of  these  vapors,  and  the  second  zone  B  is  rendered 


302  MINE  GASES  AND  VENTILATION 

luminous  by  the  incandescent  carbon  particles,  which  there 
undergo  combustion.  The  remaining  hydrogen  and  the  car- 
bon monoxide  resulting  from  this  combustion  pass  into  the 
outer  zone  C  where  they  burn  with  a  non-luminous  flame, 
supported  by  the  surrounding  air  which  here  has  free 
access  to  the  flame.  Owing  to  the  brightness  of  the  second 
zone  B,  caused  by  the  incandescence  of  the  carbon  par- 
ticles, it  is  difficult  to  discern  the  non-luminous  envelope 
surrounding  it  and  forming  the  third  zone  C. 

Flame  Caps. — 'When  a  lamp  flame  is  lowered,  almost  to  its 
point  of  extinction,  the  surrounding  air  so  closely  approaches 
the  wick  that  the  hydrocarbon  vapors  are  consumed  without 
the  incandescence  of  the  carbon.  The  dark  zone  is  here 

greatly  reduced,  while  the 
second  luminous  zone  is 
practically  eliminated,  lea- 
ving a  small  non-luminous 
flame  covering  the  wick,  as 
shown  in  the  lower  right- 
hand  corner  of  the  figure. 
Just  above,  in  the  upper 
right-hand  corner,  the 
flame  is  shown  as  slightly 

FIG  63  increased  in  size  by  raising 

the  wick   a   trifle.     There 

now  appears  a  small  luminous  zone  surmounted  by  a  non- 
luminous  cap,  which  can  be  readily  discerned.  This  cap  is 
known  as  a  "fuel  cap,"  being  due  solely  to  the  combustion  of 
the  vaporized  oil.  This  fuel  cap  is  often  mistaken  for  a  gas 
cap  when  testing  for  gas  with  a  reduced  flame. 

The  description  given  thus  far  refers  to  a  flame  burning  in 
pure  air.  Now,  when  a  lamp  flame  is  burning  in  air  charged 
with  a  small  percentage  of  a  combustible  gas,  as  methane 
for  example,  the  gas  in  contact  with  the  flame  is  consumed. 
At  the  same  time,  the  outer  zone  of  the  flame  is  lengthened  and 
rendered  more  luminous  than  before  because  of  its  increased 
size,  and  there  now  appears  what  is  known  as  the  "gas  cap" 
or  more  commonly  "flame  cap." 


MINE  LAMPS  AND  LIGHTING 


303 


The  height  of  the  flame  cap  varies  with  the  percentage  of 
gas  present  in  the  air,  the  kind  of  lamp  employed  and  the  oil 
or  luminant  burned  therein.  The  visibility  of  the  cap  is 
greatly  assisted  by  the  free  access  of  air  to  the  combustion 
chamber  of  the  lamp.  The  air  should  enter  the  lamp  at  a  point 
below  the  flame;  in  other  words,  the  ventilation  in  the  com- 
bustion chamber  should  be  ascensional.  Any  other  arrange- 
ment interferes  decidedly  with  the  clear  observance  of  the  cap. 


DIAGRAM  OF   LAMP 
FLAMES 

Top  of  Pieler  Gauze 


TABLE  GIVING  HEIGHT  OF  FLAME  CAP  OR  ELONGATION  OF  FLAME  FOR  DIFFERENT 
LAMPS  ILLUMINANTS  AND  PERCENTAGES  OF  METHANE  IN  AIR 


LAMP 

ILLUMINANT 

PERCENTAGE     OF    GAS 

>4 

k 

1    I  |!»  I  2    I  2'4l  3   1  4   |  5 

b 

HEI6HT  OF  CAP  OR   FLA 

ME.  (INCHES 

UN80NNETED 
DAVY 

SPERM.  LARD 

022 

0.43 

0.75 

1.75 

3.5* 

MNNETED 
DAVY 

SEED  OIL 

0.?2 

058 

0.88 

1.8 

3.0* 

WOLF 

NAPHTHA 

035 

0.40 

0.52 

072 

1.16 

2.76 

CLOWES 

HYDROGEN 

0.90 

1.10 

1.20 

1.40 

1.75 

2.30 

PIELER 

ALCOHOL 

1.2 

2.00 

3.00 

4DO 

5.00* 

lamp  flames  beyond  this  poini- 


^r^$i^$f^$$:$f:^$^K^^'^&» 
^  Lamp  flames  and( 


confinest>urnfgas 


PERCENTAGE    OF   METHANE     IN    AIR 

FIG.  64. 

A  dark  background  in  the  lamp  also  renders  a  cap  more  plainly 
visible. 

The  effect  of  the  form  of  the  lamp  and  the  illuminant  burned, 
to  produce  a  given  height  of  cap,  for  a  given  percentage  of  gas, 
is  clearly  shown  in  the  lamp  diagram,  Fig.  64.  The  tall  gauze 
chimney,  free  access  of  air  and  the  alcohol  burned  in  the  Pieler 
lamp  very  greatly  increase  the  height  of  the  flame,  in  the  use 
of  that  lamp,  for  the  same  percentage  of  gas  present.  On  the 
other  hand,  the  bonnet  of  the  Clowes  lamp  burning  hydrogen, 
or  the  Wolf  lamp  burning  naphtha,  materially  reduce  the 


304  MINE  GASE&  AND  VENTILATION 

height  of  flame  cap  formed  in  these  lamps,  notwithstanding 
the  volatile  nature  of  the  illuminants  burned.  The  effect  of 
the  bonnet  in  the  Davy  lamp  burning  sperm,  lard  or  cotton- 
seed oil  is  clearly  shown  to  reduce  the  height  of  the  cap,  for 
the  same  percentage  of  gas,  as  compared  with  that  obtained 
in  the  unbonneted  Davy. 

The  preceding  diagram  is  of  interest  in  connection  with  the 
use  of  different  types  of  safety  lamps  burning  hydrogen, 
alcohol,  naphtha,  or  a  non-volatile  oil,  as  sperm,  lard  or  cotton- 
seed oil,  in  testing  for  gas.  The  height  of  flame  cap,  or  the 
elongation  of  the  flame,  produced  by  different  percentages 
of  gas,  in  the  use  of  different  lamps  is  tabulated,  in  the  upper 
right-hand  corner  of  the  diagram. 

The  heights  of  flame  cap  given  in  the  diagram,  for  the  Davy 
and  Wolf  lamps,  are  the  minimum  caps  produced  by  drawing 
down  the  flame  to  its  lowest  point.  The  heights  given  for 
the  Clowes  (hydrogen)  lamp  and  the  Pieler  (alcohol)  lamp 
are  for  the  elongation  of  the  flame  due  to  the  gas.  The  original 
flame  of  the  Clowes  lamp  is  0.3  in.,  while  the  flame  of  the 
Pieler  lamp  is  adjusted  so  that  its  tip  just  reaches  the  top 
of  the  shield,  at  a  height  of  2  in.,  as  shown  in  Fig.  64.  (See 
description  of  Pieler  lamp,  p.  282.) 

The  presence  of  other  gases  or  dust  will,  of  course,  modify 
the  results  shown  in  this  diagram.  The  effect  of  carbon 
dioxide  is  to  diminish  the  length  of  the  flame  and  obstruct 
the  formation  of  the  cap.  On  the  other  hand,  carbon  monoxide 
and  dust  when  present  in  the  air  lengthen  the  flame  and  assist 
the  formation  of  a  cap. 

Calculation  of  Height  of  Flame  Cap. — For  a  Davy  lamp, 
burning  sperm  or  cottonseed  oil  of  good  quality,  in  an  atmos- 
phere charged  with  pure  methane  or  marsh  gas,  experiments 
have  shown  that  the  height  of  flame  cap  varies  as  the  cube  of 
the  percentage  of  gas  present.  Using  a  bonneted  Davy 
burning  colza  oil,  William  Galloway  has  estimated  the  height 
of  flame  cap  to  be  J'fo  of  the  cube  of  the  percentage  of  gas 
present  in  the  air  surrounding  the  lamp 

In  a  long  series  of  experiments  under  favorable  conditions, 
the  author  found  when  using  an  unbonneted  Davy  lamp 


MINE  LAMPS  AND  LIGHTING 


305 


burning  sperm  oil  the  height  of  flame  cap  was  J^g  of  the  cube 
of  the  percentage  of  gas  present  in  the  feed  air  entering  the 
lamp.  The  height  of  cap  was  accurately  measured  by  a  scale 
in  the  lamp,  and  the  percentage  of  gas  in  the  air  was  obtained 
by  the  use  of  a  Shaw  gas  machine,  which  drew  the  air  from 
the  testing  chamber  in  which  the  lamp  was  placed  and  which 
was  ventilated  by  a  continuous  current  of  air  charged  with 
the  gas.  The  arrangement  eliminated  the  effects  that  would 
otherwise  have  been  produced  by  accumulation  of  the  products 
of  combustion  in  the  lamp  chamber. 


I'-1 


4) 


42 

s:     — 


Standard': 
Reduced  Flame 


Percentage 
FIG. 


3 
of 


4 
G  a  s  in 


Air 


The  results  are  expressed  by  the  following  formulas,  giving 
the  height  of  flame  cap  h  for  any  percentage  of  gas  J: 

J3 

Unbonneted  Davy,  sperm  oil  (Beard),  h  =  ^ 

ou 

J3 

Bonneted  Davy,  colza  oil  (Galloway),  h  =  ^ 

The  appearance  of  the  flame  and  the  height  of  cap,  for  dif- 
ferent percentages  of  gas,  as  derived  from  the  author's  experi- 
ments, are  shown  in  the  illustration,  Fig.  65.  These  tests 
were  made  with  the  flame  reduced  to  a  height  of  %6  m-  It 
will  be  observed  that,  as  the  height  of  the  flame  increases, 
its  volume  is  enlarged.  At  about  3.5  per  cent,  of  gas,  the  flame 
20 


306  MINE  GASES  AND  VENTILATION          , 

became  unsteady  and,  as  the  percentage  of  gas  was  increased 
above  that  point,  the  flame  became  more  voluminous,  rotating 
in  a  wierd  manner  about  the  gauze,  then  expanding  at  the  top 
into  a  fan-shape  and  finally  filling  the  gauze  chimney  with 
flame. 

Beyond  this  point,  the  flame  has  been  frequently  seen  to 
leave  the  lampwick,  while  the  gas  continued  to  burn  in  the 
upper  portion  of  the  chimney.  When  this  occurred  with  a 
sight  indicator  in  the  lamp,  the  flame  would  relight  the  wick 
as  the  percentage  of  gas  was  reduced,  all  of  the  percentage  wires 
of  the  indicator  being  then  brightly  incandescent.  The 
same  action  has  been  observed  by  the  author  when  holding 
an  unbonneted  Davy,  equipped  with  sight  indicator,  exposed 
to  a  strong  gas  feeder.  At  that  time,  slight  explosions  occurred 
within  the  gauze,  but  the  lamp  was  not  extinguished  when 
carefully  withdrawn  from  the  gas. 

Making  a  Test  for  Gas  in  the  Mine. — When  approaching 
a  place  where  gas  is  suspected,  one  must  move  quietly  so  as 
not  to  unnecessarily  disturb  the  gas  from  its  lodgment  at  the 
roof  or  in  a  cavity.  Having  lowered  the  flame,  the  lamp  is 
cautiously  raised  into  the  gas  and  watched  for  the  first  ap- 
pearance of  a  cap  or  the  lengthening  of.  the  flame.  As  quickly 
as  this  is  observed  the  lamp  should  be  promptly  but  cautiously 
withdrawn  from  the  gas. 

On  finding  a  body  of  sharp  gas  that  has  caused  the  lamp  to 
flame,  danger  occurs  when,  in  withdrawing  the  lamp,  fresh 
air  enters  the  combustion  chamber,  creating  a  highly  explosive 
mixture  within  the  lamp.  For  this  reason,  the  lamp  must  be 
withdrawn  from  such  a  mixture  slowly  and  with  great  caution, 
which  often  requires  much  presence  of  mind.  One  should  never 
trifle  with  gas  he  has  found  in  a  cavity  of  the  roof  or  on  the 
falls. 

Gas  issuing  from  the  coal,  at  the  face  of  a  chamber,  will 
often  pass  out  in  a  thin  film  or  layer  at  the  roof,  and  may  be 
unobserved  by  a  fireboss  until  he  is  well  within  the  chamber. 
His  movement  beneath  the  layer  of  gas  may  cause  it  to  de- 
scend as  he  passes  and  he  finds,  too  late,  that  he  is  enveloped  in 
gas  from  which  he  is  able  to  escape  with  difficulty.  Under 


MINE  LAMPS  AND  LIGHTING  307 

such  circumstances,  a  fireboss  will  frequently  smother  his 
lamp  beneath  his  coat,  while  he  retraces  his  steps  cautiously. 
A  thin  layer  of  gas  at  the  roof  of  a  chamber  can  often  be 
detected  by  holding  the  lamp  erect  toward  the  roof  and  blowing 
a  slight  puff  against  the  roof,  so  as  to  cause  the  gas  to  descend 
on  the  lamp.  This  is  a  practice  followed  by  many  experienced 
firebosses.  Without  doing  so,  it  is  possible  for  a  fireboss  to 
miss  the  gas  and  report  the  place  safe  for  work  when  it  is  quite 
unsafe. 

ILLUMINANTS  FOR  SAFETY  LAMPS 

The  principal  illuminants  used  in  safety  lamps  are  the  various 
kinds  of  vegetable,  animal  and  mineral  oils.  Hydrogen  gas 
is  used  in  the  Clowes  hydrogen  lamp,  but  this  is  the  only  lamp 
burning  gas.  For  practical  purposes,  the  oils  burned  in  mine 
safety  lamps  can  be  designated  as  volatile  and  non-volatile 
oils.  A  few  testing  lamps  are  designed  to  burn  alcohol  (spirits 
of  wine),  which  is  also  a  highly  volatile  illuminant. 

Non-volatile  Oils  Used  in  Safety  Lamps. — These  are  mostly 
derived  from  the  vegetable  and  animal  kingdom.  Among  the 
vegetable  oils  largely  used  in  mining  practice  may  be  men- 
tioned cottonseed  and  colza  or  rapeseed  oil.  The  principal 
animal  oils,  which  are  also  non-volatile,  are  the  sperm,  lard, 
seal  and  whale  oils.  Of  these,  sperm  and  lard  oils  are  most 
commonly  used  in  safety  lamps  today. 

Both  vegetable  and  animal  oils  possess  less  illuminating 
power  than  mineral  oils,  and  have  a  greater  tendency  to  in- 
crust  the  wick  of  the  lamp.  They  are  more  stable,  however, 
and  the  flame  is  not  as  readily  extinguished  in  the  mine  as 
when  mineral  oil  is  burned  in  the  lamp.  The  addition  of  about 
one-half  of  their  volume  of  coal  oil  (kerosene)  greatly  improves 
the  illuminating  power  of  these  oils  but  increases  their  ten- 
dency to  smoke.  The  rate  of  burning  is  slightly  increased  and 
the  mixture  does  not  incrust  the  wick  as  rapidly  as  when  a 
pure  vegetable  or  animal  oil  is  burned. 

Mineral  Oils. — -All  mineral  oils  are  classed  under  the  general 
term,  "petroleum,"  which  is  derived  in  a  crude  state  from  the 
oil-bearing  strata.  When  the  crude  petroleum  or  "rock  oil," 


308  MINE  GASES  AND  VENTILATION 

as  it  is  sometimes  called,  is  distilled,  the  more  readily  vaporized 
hydrocarbon  vapors  condense  on  cooling  to  what  are  termed  light 
or  volatile  oils.  These  are  distilled  at  temperatures  below 
300  deg.  F.  Coal  oil,  or  kerosene,  is  the  product  distilled  be- 
tween 300  and  570  deg.  F.,  while  the  heavy  lubricating  oils 
are  distilled  at  still  higher  temperatures.  These  last  products 
contain  paraffin,  which  is  separated  from  the  heavy  oils  by 
its  solidifying  at  130  deg.  F.,  in  cooling.  Of  the  light  oils, 
gasoline  is  distilled  below  140  deg.,  naphtha,  below  230  deg., 
and  benzine,  below  300  deg.  F. 

Light,  Volatile  Oils. — The  danger  in  the  use  of  light  volatile 
oils,  as  illuminants  in  safety  lamps,  arises  from  their  low  flash- 
ing points.  The  ready  vaporization  of  the  oil,  as  the  lamp 
heats  in  gas,  renders  the  test  for  gas  unreliable  in  the  use  of  a 
lamp  burning  such  an  oil.  The  storing  of  a  highly  volatile  oil 
at  a  mine  and  the  filling  of  the  lamps  in  the  lamphouse  requires 
extra  precautions  to  be  taken  to  avoid  accident.  In  order  to 
reduce  the  danger  of  its  use  in  the  lamp,  the  oil  vessel  is 
filled  with  absorbent  or  filling  cotton.  A  light  volatile  oil  is 
not  as  stable  as  a  vegetable  or  animal  oil,  and  its  flame  is 
more  easily  extinguished  when  such  an  oil  is  used  in  the  mine. 
A  volatile  oil  flame,  however,  is  more  sensitive  to  gas  and  has 
a  higher  illuminating  power  than  other  oils,  which  has  favored 
its  use  in  many  mining  districts. 

MINERS'  CARBIDE  LAMPS 

The  acetylene  or  carbide  lamp  that  has  come  into  such  ex- 
tensive use  in  coal  mining,  within  the  past  few  years,  is  an 
open-flame  lamp  constructed  to  burn  acetylene  gas,  generated 
within  the  lamp,  by  the  slow  feeding  of  water  onto  the  carbide. 
The  water  and  the  carbide  are  contained  in  two  separate  com- 
partments of  the  lamp. 

The  supply  of  water  to  the  carbide  is  regulated  by  a  valve 
having  a  screw  adjustment  at  the  top  of  the  lamp.  The  water 
is  contained  in  the  upper  half  of  the  lamp  and  the  carbide  in 
the  compartment  below.  The  latter  should  not  be  more  than 
half  filled  with  the  carbide,  which  swells  when  moistened  with 


MINE  LAMPS  AND  LIGHTING 


309 


the  water.  A  charge  of  2J£  oz.  of  carbide  will  supply  gas  suffi- 
cient to  maintain  a  flame  1J^  in.  in  length  during  a  half -shift 
or  more  but  then  it  will  be  necessary  to  recharge  the  lamp. 

Owing  to  the  brightness  of  the  acetylene  flame,  the  carbide 
lamp  has  very  largely  replaced  the  old  open-flame  torch  so 
commonly  used  in  mines  generating  no  gas.  The  general  form 
of  carbide  lamp  in  common  use  is  shown  in  Fig.  66,  although 
there  are  different  styles  of  this  lamp  manufactured,  some  hav- 
ing no  reflectors  behind  the  flame  and  differing  in  other 
details.  The  lamp  shown  in  the  figure  is  a  type  very  largely 

used    in    the    anthracite    district. 

Most  of  these  lamps  in  use  differ 
only  in  slight  details. 

Generation  of  Acetylene  Gas.— 
Carbide  (CaC2)  is  a  product  of  the 
action  of  coke  on  quicklime,  calcium 
oxide  (CaO).  The  lime  and  coke 
are  finely  ground,  thoroughly  mixed 
and  heated  to  a  white  heat  in  an 
electric  furnace.  Under  the  high 
heat  of  this  furnace  a  portion  of 
the  carbon  unites  with  the  calcium 
to  form  calcium  carbide  (CaC2),  the 
remainder  of  the  carbon  taking  up  the  oxygen  and  passing  off 
as  carbon  dioxide  (CO*),  according  to-  the  reaction, 

4CaO  +  5C2  =  4CaC2  +  2CO2 

When  water  comes  in  contact  with  calcium  carbide,  calcium 
hydroxide,  Ca(OH)2,  is  formed  and  acetylene  gas  (C2H2)  is 
set  free  according  to  the  equation. 

CaC2  +  2H2O  =  Ca(OH)2  +  O2H2 

The  acetylene  gas  is  highly  inflammable  and  when  ignited 
in  the  air  burns,  producing  carbon  dioxide  and  water  vapor. 
Ignoring  the  inert  nitrogen  of  the  air,  this  reaction  is  expressed 
by  the  following  equation : 


FIG.  68. 


2C2H2  +  5O2  =  4CO2  +  2H2O 


310  MINE  GASES  AND  VENTILATION 

One  ounce  of  pure  crystallized  calcium  carbide  will  generate 
622  cu.  in.  of  acetylene  gas,  measured  at  a  normal  temperature 
of  60  deg.  F.,  barometer  30  in.  Commercial  carbide,  however, 
will  commonly  yield  only  from  400  to  500  cu.  in.  per  ounce  of 
carbide  used,  depending  on  the  completeness  of  its  consump- 
tion in  the  lamp. 

Burning  Acetylene  Gas. — For  the  purpose  of  estimate,  it 
may  be  assumed  that  an  average  miner's  carbide  lamp  con- 
sumes H  °z-  °f  carbide  per  hour  and  generates  250  cu.  in. 
of  acetylene  gas.  Then,  since  one  volume  of  this  gas,  in 
burning,  consumes  2J^  volumes  of  oxygen  or,  say  12^  volumes 
of  air  and  produces  2  volumes  of  carbon  dioxide  and  1  volume 
water  vapor,  the  burning  of  a  carbide  lamp  may  be  estimated 
as  producing  500  cu.  in.  of  carbon  dioxide  and  half  that  volume 
of  water  vapor,  per  hour.  In  the  same  time,  the  lamp  takes 
from  the  air  625  cu.  in.  of  oxygen,  leaving  practically  2500  cu. 
in.  of  excess  nitrogen. 

The  effect  of  the  burning  of  a  carbide  lamp  to  vitiate  the 
mine  air  is  thus  seen  to  be  inappreciable  and  far  less  than  the 
breathing  of  a  man,  who  consumes  little  short  of  1000  cu.  in. 
of  oxygen,  per  hour,  when  at  rest,  and  over  8000  cu.  in.  per 
hr.,  in  violent  exercise,  and  exhales  an  equal  volume  of  air 
containing  from  2J^  to  6^  per  cent,  of  carbon  dioxide. 

Calculation. — The  molecular  weight  of  calcium  carbide 
(CaC2)  being  40  +  2(12)  =  64;  and  that  of  acetylene  (C2H2), 
2(12  -}-  1)  =  26;  and  the  specific  gravity  of  this  gas  referred 
to  air  being  0.92,  we  have  the  following: 

Weight  of  1  cu.  ft.  air  (60  deg.  F.,  bar.  30  in.) .  .   0.0766  lb. 

Weight  of  1  cu.  ft.  acetylene,  0.92(0.0766) 0.07047  lb. 

Volume  of  1  lb.  acetylene 

(60  deg.  F.,  bar.  30  in.)  M.07047-  •  •  -14.19  cu.fi. 

14  19  X  1728 
Volume  of  1  oz.  acetylene  -        ^       — . . . .  1532.5  cu.  in. 

Then,  since  64  parts,  by  weight,  of  calcium  carbide  yield 
26  parts,  by  weight,  of  acetylene  gas,  one  ounce  of  the  pure 

crystallized  carbide  will  generate 
f)(* 
^  (1532.2)  =  622  +  cu.  in.  acetylene, 

measured  at  60  deg.  F.,  bar.  30  in. 


MINE  LAMPS  AND  LIGHTING  311 

Properties  of  Acetylene  Gas. — The  gas  is  colorless  and  has  a 
strong  pungent  odor,  due  to  the  presence  of  some  sulphureted 
and  phosphureted  hydrogen,  as  generated  in  the  carbide  lamp, 
by  the  action  of  water  on  the  carbide.  It  has  a  specific 
gravity  of  0.92,  referred  to  air  at  the  same  temperature  and 
pressure.  Under  atmospheric  pressure,  the  gas  liquefies 
at  —  115  deg.  F.,  the  volume  of  the  liquid  being  Hoo  of  that 
of  the  original  gas. 

Acetylene  gas  is  combustible,  igniting,  in  contact  with  air, 
at  a  temperature  of  900  deg.  F.  When  the  gas  is  largely  in 
excess  and  the  supply  of  air  limited  the  acetylene  is  smoky 
and  deposits  soot,  but  when  a  fine  stream  of  the  gas  is  spurted 
into  the  air,  as  in  the  carbide  lamp,  a  flame  of  exceeding  bril- 
liancy is  the  result.  Owing  to  its  low  temperature  of  ignition, 
the  gas  can  be  ignited  by  a  lighted  cigar. 

Mixed  with  air  the  gas  becomes  highly  explosive  its  explo- 
sive range  being  wider  than  that  of  any  other  gas.  While 
the  inflammable  range  of  hydrogen  extends  from  5  to  72  per 
cent.,  that  of  acetylene  ranges  from  3  to  82  per  cent.,  as  de- 
termined by  Clowes.  This  high  value  for  the  upper  explosive 
limit  has  not  been  obtained  by  other  investigators,  whose 
results  vary  from  50  per  cent.  (Federal  Bureau  of  Mines) 
to  65  per  cent.  (LeChatelier). 

The  Carbide  Lamp  in  Blackdamp. — What  is  known  as 
"blackdamp"  in  mining  is  a  variable  mixture  of  carbon 
dioxide  and  air  deficient  in  oxygen;  in  other  words,  an 
atmosphere  of  blackdamp  consists  of  nitrogen,  oxygen  and 
carbon  dioxide  in  varying  proportions.  When  carbon  dioxide 
is  generated  in  a  mine  ventilated  by  an  ample  air  current 
containing  a  normal  percentage  (20.9%)  of  oxygen  the  addi- 
tion of  any  considerable  amount  of  carbon  dioxide  to  this 
normal  air  reduces  the  oxygen  content  by  the  dilution  of  the 
air  with  the  gas.  The  air  is  then  said  to  be  "deficient  in 
oxygen,"  which  is  due  solely  to  its  dilution  with  the  carbon 
dioxide. 

On  the  other  hand  a  much  greater  reduction  of  the  oxygen 
content  often  occurs  when  a  portion  of  the  oxygen  has  been 
consumed  by  the  various  forms  of  combustion  that  are  con- 


312  MINE  GASE8  AND  VENTILATION 

stantly  taking  place  in  the  mine.  It  -is  this  reduction  of  the 
oxygen  content,  or  the  "  depletion  of  oxygen"  in  the  mine 
air  that  is  most  harmful  to  life  and  affects  the  burning  of 
the  lamps. 

It  is  a  well  known  fact  that  the  carbide  lamp  will  continue 
to  burn  in  air  deficient  in  oxygen  when  oil-fed  flames  and 
the  hydrogen  flame  are  quickly  extinguished.  The  acetylene 
gas  burned  in  the  carbide  lamp  is  generated,  in  the  lamp,  by 
the  action  of  water  on  the  carbide  of  calcium,  the  calcium 
taking  the  oxygen  and  some  of  the  hydrogen,  while  the 
carbon  takes  the  remaining  portion  of  the  hydrogen. 

We  cannot  say  but  that,  in  the  dissociation  of  the  hydro- 
gen and  oxygen  of  the  water  (H^O) ,  some  oxygen  may  go  to 
support  the  combustion  of  the  acetylene  gas  (C^Hy,  instead 
of  the  flame  being  wholly  dependent  on  the  oxygen  of  the 
air  for  support.  However,  it  is  safe  to  say  that  an  atmos- 
phere in  which  a  carbide  continues  to  burn  may  be  danger- 
ous to  life  and  therefore  unsafe  for  work. 

In  an  atmosphere  containing  no  carbon  dioxide,  the  oxygen 
content  may  fall  as  low  as  14  per  cent,  before  much  difficulty 
is  experienced  in  breathing;  but  air  containing  but  10  per 
cent,  is  no  longer  breathable  and  will  cause  death  quickly  by 
suffocation." 

The  toxic  effect  of  carbon  dioxide  is  clearly  shown  by  the 
fact  that  the  depletion  of  the  oxygen  content  of  air,  by  the 
addition  of  carbon  dioxide,  produces  a  fatal  atmosphere  when 
the  oxygen  is  reduced  to  but  17  per  cent.;  while,  if  no  car- 
bon dioxide  is  present,  a  fatal  atmosphere  is  produced  only 
when  the  depletion  of  the  oxygen  reaches  10  per  cent. 

In  the  former  of  these  two  cases,  there  is  but  83  per  cent, 
of  noxious  gases  present — carbon  dioxide,  18  per  cent,  and 
nitrogen,  65  per  cent.;  while,  in  the  latter  case,  there  is  90 
per  cent,  of  nitrogen  present.  In  the  former  case  a  depletion 
of  oxygen  to  17  per  cent,  marks  a  fatal  atmosphere;  while 
in  the  latter  case,  a  depletion  of  oxygen  to  10  per  cent,  is 
necessary  to  produce  the  same  result. 

It  is  quite  doubtful  if  a  carbide  lamp  is  extinguished  when 
the  oxygen  of  the  atmosphere  is  reduced  to  14  per  cent.,  as 
is  frequently  assumed. 


MINE  LAMPS  AND  LIGHTING  313 

Precautions  to  be  Taken. — In  the  use  of  carbide  lamps  in 
mines,  suitable  rules  and  regulations  should  be  made  and 
enforced  limiting  the  supply  of  carbide  that  a  miner  may  carry 
into  the  mine  to  what  is  ample  for  his  purpose  in  a  single 
shift  and  prohibiting  its  careless  use.  A  supply  of  carbide 
should  never  be  permitted  to  be  stored  in  a  miner's  box  or 
elsewhere  in  a  mine.  With  proper  care  and  precautions  there 
need  be  little  fear  of  trouble.  The  carbide  light  being  an  open- 
flame  lamp  should  not  be  used  in  a  mine  generating  gas. 

ELECTRIC  MINE  LAMPS 

The  electric  mine  lamp  is  now  almost  universally  used  in 
all  up-to-date  mines  in  the  states  and  Canada,  there  being  at 
present  150,000  of  these  lamps  installed  by  the  Edison  Storage 
Battery  Co.  alone.  Of  this  number,  80,000  of  the  lamps  are 
in  daily  use  in  the  mines  of  Western  Pennsylvania. 

Selecting  a  Suitable  Battery .-^In  the  endeavor  to  provide  a 
portable  electric  mine  lamp  that  would  meet  the  require- 
ments of  mine  service,  the  chief  difficulty  was  to  find  a  bat- 
tery that  would  be  sufficiently  light  and  have  the  necessary 
watt-hour  capacity  to  furnish  a  good  light  a  full  8-hr,  shift. 

All  forms  of  primary  batteries  that  depend  on  the  chemical 
reaction  set  up  between  certain  elements  immersed  in  a  solu- 
tion, as  well  as  the  lead-sulphuric  acid  storage  battery,  proved 
unsuited  to  service  in  the  mine.  The  lead-lead  battery  was 
too  heavy,  besides  failing  in  other  ways  to  meet  the  requirements 
of  mining  use.  Even  the  substitution  of  a  gelatinous  elec- 
trolyte proved  ineffectual,  owing  to  the  hardened  jelly  not 
absorbing  the  water  when  once  dried  and  the  crack  becoming 
filled  with  sediment  short-circuiting  the  cells  and  weakening 
the  battery. 

The  Edison  Storage  Battery.— The  difficulties  just  men- 
tioned have  been  practically  overcome  in  the  Edison  storage 
battery  designed  for  mine  use.  This  battery  employs  as 
elements  nickel  hydroxide  and  iron  oxide  immersed  in  a  potash 
solution.  The  battery  cells  are  incased  in  a  strong  nickel- 
plated  steel  container,  which  is  tightly  sealed  except  for  one 


314 


MINE  GASES  AND  VENTILATION 


small  vent  being  left  for  the  escape  of  the  harmless  gases  that 
result  in  the  charging  of  the  battery. 

The  illustration,  Fig.  67,  shows  the  two  cells  of  the  Edison 
mine-lamp  battery  removed  from  the  iiickeled-steel  case. 
The  steel  container  of  one  cell  is  cut  away  to  show  the  interior 
arrangement.  The  positive  plates  (steel  tubes  of  nickel 
hydrate)  and  the  negative  plates  (steel  pockets  of  iron  oxide) 
are  assembled  on  steel  poles  and  intermeshed,  which  gives  an 
exceptionally  strong  and  compact  construction  entirely  of 
steel,  there  being  no  acid  to  cause  corrosion. 

The  construction  of  this 
battery  is  such  that  it  is 
practically  impossible  for 
the  solution  to  find  its  way 
out,  even  should  the  battery 
be  turned  upsidedown ;  and 
no  injury  can  result  from  a 
possible-  overcharging,  or 
from  leaving  the  cell  in  a 
charged,  semi-charged  or 
discharged  condition,  for 
an  indefinite  period .  While 
the  cell  must  be  charged  in 
the  right  direction  to  be  fit 
for  service,  no  injury  can 
result  from  accidentally 
reversing  this  direction. 
The  steel  container  is  proof  against  rough  usage,  and  no  in- 
sulation troubles  can  occur.  Specific  gravity  tests  are  not  re- 
quired as  the  potash  solution  is  renewed  after  9  or  10  months 
of  use  in  continuous  daily  service. 

Cap  Lamp  and  Connecting  Cable. — The  illustration,  Fig. 
68,  shows  the  electric  cap  lamp  and  the  nickeled-steel  carrying 
case  holding  two  cells.  The  cover  of  the  case  is  removed  to 
show  the  steel  contact  plates  affixed  to  but  insulated  from  the 
cover.  These  plates  connect  with  the  contact  springs  shown 
mounted  on  the  two  terminals  of  the  battery.  The  cover  is 
secured  to  the  case  by  a  strong  hasp  and  padlock.  To  this 


FIG.  67. 


MINE  LAMPS  AND  LIGHTING 


315 


cover  is  attached  a  twin-conductor,  rubber-covered  cable, 
armored  at  both  ends  to  prevent  injury  where  sharp  bending 
is  liable  to  occur.  If  injured  the  cable  is  easily  replaced. 

The  supporting  base  of  the  lamp  is  a  nickel-plated  reflector 
having  a  highly  finished  surface  and  provided  with  a  hook  to 
fit  into  the  regulation  miner's  cap.  The  angle  of  distribution 
is  considerably  greater  than  the  130  deg.  specified  by  the 
government,  (see  p.  322).  A  tungsten  lamp  is  forced  into 
a  spring  socket  by  means  of  a  clip  at  its  tip  in  such  a  way 
that  if  the  lamp  should  be  broken  the  base  is  immediately 
disconnected  and  the  lamp  extinguished.  This  safety  feature 
has  been  thoroughly  tested  by  the  Bureau  of  Mines  and  un- 


FIG.  68. 

qualifiedly  approved  under  Schedule  6A.  In  place  of  a  lens 
is  a  plain  glass  that  is  easily  replaced  if  broken.  The  entire 
design  is.  such  as  to  afford  the  greatest  possible  headroom 
clearance. 

Charging  Miners'  Lamp  Batteries. — The  recharging  of  a 
large  number  of  lamp  batteries,  between  shifts,  calls  for  a 
special  design  of  equipment  that  will  provide  at  once  for  the 
charging  of  the  batteries  and  enumerating  them  so  that  any 
individual  battery  can  be  found  without  delay. 

A  convenient  form  of  charging  rack  that  meets  these  require- 
ments is  one  built  up  on  the  unit  system,  corresponding  to  the 
sectional  bookcase  idea.  The  illustration,  Fig.  69,  is  a  view 
of  such  a  rack,  designed  and  built  by  the  Cutler-Hammer  Mfg. 


316 


MINE  GASES  AND  VENTILATION 


Co.,  Milwaukee,  Wis.  The  figure  shows  four  units,  but  the 
system  can  plainly  be  extended  indefinitely  to  accommodate 
an  increasing  number  of  lamps  as  the  development  of  the  mine 
proceeds.  The  recharging  room  must  be  well  ventilated  and 
open  lights  should  not  be  permitted. 


FIG.  70. 

On  the  right  of  the  figure  are  shown  two  rheostat  panels  and 
a  meter  panel  above.  These  panels  are  shown  in  greater  de- 
tail in  the  Fig.  70,  together  with  front  and  top  views  of  a 
single  unit  capable  of  holding  ten  lamp  batteries  for  charging. 


MINE  LAMPS  AND  LIGHTING  317 

The  contact  parts  supported  by  the  upper  slab  are  pressed 
down  in  contact  with  the  battery  by  the  coil  springs  above  the 
slab.  The  batteries  are  charged  in  series  and  provision  is 
made  for  interpolating  resistances  to  take  the  place  of  one  or 
more  absent  batteries. 

Pipe  columns  to  which  are  clamped  supporting  brackets, 
as  shown  in  this  figure,  form  the  framework  of  the  rack  on 
which  are  hung  the  several  battery  units  and  panels  by  means 
of  the  strong  hooks  shown  attached  to  each. 

Each  rheostat  panel  is  designed  to  control  the  current  in 
the  corresponding  line  of  units,  and  is  equipped  with  a  sliding 
arm  for  adjusting  the  charging  rate  to  any  desired  value. 
The  double-pole  knife  switch  shown  on  this  panel  is  so  arranged 
that  when  partly  closed  the  ammeter  on  the  meter  panel  is 
thrown  into  circuit;  but  when  closed  completely  the  ammeter 
is  cut  out  and  the  current  passed  through  the  charging  racks. 

The  meter  panel  not  only  holds  the  ammeter  for  measuring 
the  strength  of  the  current  and  regulating  it  in  accordance  with 
the  number  of  units  to  be  charged ;  but  is  also  provided  with  a 
magnetic  switch  and  compound  relay,  which  prevents  a  rever- 
sal of  current  from  the  partially  charged  batteries  taking  place 
should  the  charging  current  be  interrupted  for  a  time.  This 
device  automatically  opens  and  closes  the  circuit  as  the  cur- 
rent is  broken  and  again  restored.  The  breaking  of  the  current 
is  immediately  announced  by  the  signal  bell  on  each  rheostat 
panel. 

Edison  mine-lamp  batteries  require  a  pressure  of  40  volts, 
which  makes  it  possible  to  charge  six  10-battery  units,  on  a 
250-volt  circuit.  However,  it  is  generally  advisable  to  install 
but  five  such  units  on  this  circuit,  which  would  allow  the  pres- 
sure to  drop  to  200  volts  without  interrupting  the  charging. 

Use  of  the  Electric  Cap  Lamp.  — The  need  of  a  reliable  source 
of  illumination  in  mining  work  has  long  been  sought  but  with 
limited  success.  Open-flame  lamps  or  torches  are  necessarily 
restricted  to  non-gaseous  mines,  or  where  the  conditions  are 
such  as  not  to  require  the  exclusive  use  of  safety  lamps.  On 
the  other  hand,  the  relatively  dim  light  of  a  safety  lamp  and 
its  lack  of  adaptation  to  the  requirements  of  mining  work  make 


318  MINE  GASES  AND  VENTILATION 

it  always  desirable  to  find  a  suitable  substitute  that  will  be 
both  convenient  and  safe  for  general  work. 

The  electric  cap  lamp  with  storage  battery  equipment  simi- 
lar to  that  shown  in  the  illustration,  Fig.  71,  has  apparently 
solved  the  problem,  and  furnished  the  miner  with  a  good  light 
that  is  convenient  and  safe.  The  principal  objections  that 
have  been  urged  against  the  miners'  electric  lamp  are  the 
slightly  increased  cost  of  the  equipment,  and  the  fact  that  an 


FIG.  71. 

electric  lamp  affords  no  indication  of  the  presence  of  gas, 
either  methane  or  blackdamp,  and  gives  the  miner  no  warning 
of  danger  in  that  respect. 

Notwithstanding  these  disadvantages,  the  electric  lamp  has 
steadily  grown  in  favor  among  miners,  as  shown  by  its  general 
adoption  and  successful  use.  In  daily  practice,  the  miner 
straps  the  battery  case  to  his  back,  by  his  ordinary  belt.  The 
lamp  is  attached  to  the  leather  support  in  his  cap,  leaving  his 


MINE  LAMPS  AND  LIGHTING  319 

arms  entirely  free  of  lamp,  cord  and  battery  case.  When  the 
case  is  locked  and  the  equipment  handed  to  the  miner  charged 
and  ready  for  use  there  can  be  no  safer  or  surer  means  of 
illumination. 

PERMISSIBLE  PORTABLE  ELECTRIC  MINE  LAMPS 

Schedule  6A,  issued  by  the  Federal  Bureau  of  Mines,  defines 
what  is  to  be  understood  as  included  under  the  appellation 
"Permissible,"  in  reference  to  portable  electric  mine  lamps,  in 
the  following  words: 

The  Bureau  of  Mines  considers  a  portable  electric  lamp  to  be  per- 
missible for  use  in  mines  if  all  the  details  of  the  lamp's  construction 
are  the  same,  in  all  respects,  as  those  of  the  lamp  that  passed  the  in- 
spection and  the  tests  for  safety,  practicability,  and  efficiency  made 
by  the  bureau  and  hereinafter  described. 

Conditions  of  Testing. — The  conditions  under  which  the  Bureau  of 
Mines  will  examine  and  test  portable  electric  lamps  to  establish  their 
permissibility  are  as  follows: 

1.  The  tests  will  be  made  at  the  experiment  station  of  the  Bureau  of 
Mines  at  Pittsburgh,  Pa. 

2.  Applications  for  tests  shall  be  addressed  to  the  Director,  Bureau 
of    Mines,   Washington,   D.   C.,   and  shall  be  accompanied  by  a  com- 
plete  description  of  the  lamp  to  be  tested  and  a  full  set 'of  the  draw- 
ings mentioned  below. 

A  drawing  or  drawings  clearly  showing  the  size  and  general  appear- 
ance of  the  lamp  mounting. 

A  drawing  or  drawings  clearly  showing  the  character,  size  and  relative 
arrangement  of  the  parts  of  the  lamp  mounting  and  the  principle  of 
operation  of  the  safety  devices. 

Any  other  drawings  that  may  be  necessary  to  identify  the  safety 
devices  or  to  explain  how  they  accomplish  their  purpose. 

A  copy  of  the  description,  a  duplicate  of  the  drawings  and  one  complete 
lamp  shall  be  sent  to  the  Electrical  Engineer,  Bureau  of  Mines,  Fortieth 
and  Butler  Streets,  Pittsburgh,  Pa. 

3.  As  soon  as  possible,  after  the  receipt  of  his  application  for  test, 
the  lamp  manufacturer  will  be  notified  of  the  date  on  which  his  lamps 
will  be  tested  and  the  amount  of  material  that  it  will  be  necessary  for 
him  to  submit. 

4.  All   material  for  test  shall  be  delivered  by  the  manufacturer  to 
the  Electrical  Engineer,  Bureau  of  Mines,  Fortieth  and  Butler  Streets, 
Pittsburgh,  Pa.,  not  less  than  one  week  prior  to  the  date  set  for  the 
test. 


320  MINE  GASES  AND  VENTILATION 

5.  No  lamp  equipment  will  be  tested,  unless  it  is  in  the  completed 
form  in  which  it  is  to  be  put  on  the  market. 

6.  Lamps  so  constructed  that  they  can  be  used  both  as  cap  lamps 
and  as  hand  lamps  must  pass  the  tests  for  both  cap  lamps  and  hand 
lamps  or  they  will  not  be  approved  for  either  class  of  service. 

7.t  No  one  is  to  be  present  at  these  tests,  except  the  necessary  govern- 
ment officers,  their  assistants,  and  one  representative  of  the  manufacturer 
of  the  lamp  to  be  tested,  who  shall  be  present  in  the  capacity  of  an  ob- 
server only. 

The  conduct  of  the  tests  shall  be  entirely  in  the  hands  of  the  bureau's 
engineer  in  charge  of  the  investigation.  While  the  tests  are  in  progress 
the  manufacturer's  representative  shall  not  make  unsolicited  suggestions 
or  criticismsof  the  method  of  conducting  the  test. 

8.  The  tests  will  be  made  in  the  order  of  the  receipt  of  application 
for  test,   provided  that  the  necessary  lamp  equipment  is  submitted 
at  ohe  proper  time. 

9.  The  details  of  the  results  of  the  tests  shall  be  regarded  as  con- 
fidential by  all  present  at  the  tests,  and  shall  not  be  made  public,  in 
any  way,  prior  to  their  official  publication  by  the  Bureau  of  Mines. 

Requirements  for  Approval. — The  requirements  that  a  portable  electric- 
lamp  equipment  must  have,  to  pass  successfully  the  inspection  and  tests 
required  by  the  bureau,  are  stated  below : 

1.  The  lamp  equipment  must  comply  with  the  following  require- 
ments for  mechanical  and  electrical  construction : 

The  construction  of  permissible  portable  electric-lamp  equipment 
shall  be  especially  durable.  All  parts  shall  be  constructed  of  suitable 
material  of  the  best  quality  and  shall  be  assembled  in  a  thorough. work- 
manlike manner.  Current-carrying  parts  shall  be  well  insulated  from 
parts  of  opposite  polarity  and  from  parts  not  intended  to  carry  current. 

The  battery  shall  be  inclosed  in  a  locked  or  sealed  box  so  constructed 
as  to  preclude  the  possibility .  of  anyone  meddling  with  the  electrical 
contacts  or  making  an  electrical  connection  with  them  while  the  box  cover 
is  closed. 

The  leads  connecting  the  battery  with  the  headpiece  shall  be  made 
up  in  a  single  cable  efficiently  insulated  and  provided,  where  it  leaves 
the  battery  casing  and  enters  the  headpiece,  with  a  reinforcement  of 
flexible  metallic  tubing.  The  flexible  metallic  tubing  will  not  be  re- 
quired if  other  equally  durable  means  of  reinforcement  are  provided. 

It  is  recommended,  but  not  required,  that  the  headpiece  be  so  de- 
signed that  it  can  be  sealed  or  locked.  The  battery  terminals  and 
leads  connecting  thereto,  and  the  gas  vent  of  the  battery  shall  be  so 
designed  and  constructed  as  to  prevent  corrosion  of  the  battery  ter- 
minals or  of  the  essential  metallic  parts  mounted  in  the  cover  of  the 
battery  casing. 

The  following  qualities  will  be  considered  in  determining  the  excel- 


MINE  LAMPS  AND  LIGHTING  321 

lence  of  the  mechanical  and  electrical  construction  of  lamps  covered 
by  these  specifications: 

Simplicity  of  design;  mechanical  strength  of  parts  and  fastenings; 
suitability  of  material  used;  design  of  moving  and  removable  parts; 
design  and  construction  of  terminals  and  contacts,  for  permanence 
and  electrical  efficiency ;  and  ease  of  repair. 

2.  The  lamp  equipment  must  be  provided  with  a  safety  device  or 
devices  as  follows: 

Permissible  portable  electric  lamps  shall  be  so  designed  and  constructed 
that  whenever  the  bulb  of  a  completely  assembled  lamp  equipment 
is  broken  the  lamp  filament  shall,  at  once  and  under  all  circumstances, 
cease  to  glow  at  a  temperature  that  will  ignite  explosive  mixtures  of  mine 
gas  and  air. 

The  mounting  of  the  bulb  may  be  designed  so  that  a  blow  sufficient 
to  break  the  bulb  will  short-circuit  it,  open  the  electric  circuit  of  the 
lamp  or  otherwise  insure  that  the  filament  will  be  wholly  or  practically 
extinguished.  All  safety  devices  with  which  the  lamps  are  provided 
shall  be  so  completely  protected  from  injury  or  disturbance  as  to  insure 
that  the  devices  will  always  be  in  condition  to  perform  their  functions. 

The  design  of  the  safety  features  shall  be  such  that  their  action  can 
not  readily  be  hindered  or  prevented.  The  design  of  the  safety  devices 
shall  be  such  that  they  will  not  act  to  extinguish  the  lamp  unnecessarily. 

3.  The  lamp  equipment  must  be  provided  with  a  battery  having  a 
short-circuit  current  not  in  excess  of  the  values  here  specified. 

The  bureau's  engineers  have  made  tests  (reported  in  Technical  Paper 
47  of  the  bureau),  which  have  satisfied  them  that  mine  gas  can  not  be 
ignited  by  the  sparks  from  portable  electric-lamp  equipments  if  the 
batteries  used  with  such  equipments  are  made  so  that  their  maximum 
short-circuit  current  can  not  exceed  the  following  values :  For  batteries 
giving  2.5  volts  or  less,  125  amperes;  for  batteries  giving  more  than 
2.5  volts  but  not  more  than  4  volts,  85  amperes;  for  batteries  giving 
more  than  4  volts  but  not  more  than  5  volts,  65  amperes;  for  batteries 
giving  more  than  5  volts  but  not  more  than  6  volts,  45  amperes.  There- 
fore, lamps  whose  short-circuit  current  does  not  exceed  these  values  will 
be  considered  satisfactory  in  that  respect. 

4.  The  lamp  equipment  must  meet  the  following  requirements  for 
time  of  burning,  flux  of  light,  intensity  of  light  and  distribution  of  light: 

All  portable  electric  lamps  offered  for  test  under  the  provisions  of 
this  schedule  shall  produce,  for  12  consecutive  hours,  on  one  charge  of 
battery,  a  light  stream  having  an  averge  intensity  of  light  not  less  than 
four-tenths  of  a  candlepower.  The  to'al  flux  of  light  produced  by 
cap  lamps  shall  not  fall  below  IK  lumens  during  the  12  hours,  and  the 
total  flux  of  light  produced  by  hand  lamps  shall  not  fall  below  3  lumens 
during  the  12  hours. 

The  distribution  of  light,  by  lamps  that  use  reflectors,  shall  be  deter- 
mined both  by  observation  and  by  photometric  measurement.  The 

21 


322  MINE  OASES  AND  VENTILATION 

lamps  shall  be  placed  so  that  the  filaments  are  20  in.  away  from  a  plane 
surface  that  is  perpendicular  to  the  axis  of  the  light  stream  of  the  lamp. 
When  so  placed  the  lamp  shall  illuminate  a  circular  area  not  less  than 
7  ft.  in  diameter.*  All  observations  and  measurements  of  distribution 
shall  be  referred  to  this  7-ft.  circle  regardless  of  how  large  an  area  the 
lamp  may  illuminate.  As  observed  with  the  eye,  there  shall  be  no 
"black  spots"  within  the  7-ft.  circle,  nor  any  sharply  contrasting  areas 
of  bright  and  faint  illumination  anywhere.  As  measured  with  a  photo- 
meter, the  distribution  of  light  diametrically  across  the  circle  shall  fulfill 
the  following  requirements: 

The  curve  of  light  distribution  along  the  diameter  of  the  circle  shall 
be  obtained  by  rotating  the  lamp  and  thus  obtaining  the  average  distri- 
bution curve. 

The  average  illumination  in  foot-candles,  on  the  best  illuminated 
one-tenth  of  the  diameter,  shall  be  not  more  than  three  times  the  average 
illumination  throughout  the  diameter;  and,  for  at  least  40  per  cent, 
of  the  diameter,  the  illumination  shall  be  not  less  than  the  average. 

5.  The   lamp   equipment   must  be   provided   with  lamp   bulbs  that 
meet  the  following  requirements,   for  variation  in   current  consump- 
tion, variation  in  candlepower  and  length  of  life : 

The  bulbs  submitted  for  test  shall  be  identified  by  the  name  of  the 
manufacturer  and  by  a  number  or  symbol  with  reference  to  which 
approval  will  be  granted. 

The  current  consumption  of  at  least  95  per  cent,  of  the  bulbs  tested 
shall  not  exceed,  by  more  than  6  per  cent.,  the  average  current  con- 
sumption of  all  the  bulbs  examined. 

The  candlepower  of  at  least  90  per  cent,  of  the  bulbs  tested  shall 
not  fall  short  of  the  average  candlepower,  by  more  than  30  per  cent. 

The  life  of  a  lamp  bulb  will  be  considered  as  the  number  of  hours  that 
the  bulb  can  be  burned,  under  normal  conditions  of  voltage,  before  it 
becomes  so  depreciated  that  when  used  with  an  average,  standard, 
freshly  charged  equipment  it  fails  bo  produce,  for  12  consecutive  hours, 
the  flux  and  intensity  of  light  specified  in  paragraph  4. 

The  average  life  of  lamp  bulbs  shall  be  not  less  than  300  hours,  for 
acid  storage  batteries,  and  not  less  than  200  hours,  for  primary  batteries 
and  for  alkaline  storage  batteries.  Not  more  than  5  per  cent,  of  the 
bulbs  examined  shall  give  less  than  250  hours'  life,  with  acid  batteries, 
nor  less  than  150  hours'  life,  with  primary  batteries  and  alkaline  batteries. 

6.  The  lamp  equipment  must  comply  with  the  following  requirements 
as  to  leakage  of  electrolyte : 

Lamps  shall  be  so  designed  and  constructed  that  they  will  not  spill 
nor  leak  electrolyte  throughout  an  8-hour  test,  during  which  they  will  be 
placed  in  any  position  or  sequence  of  positions  that,  in  the  opinion  of  the 
bureau's  engineers,  will  be  most  likely  to  prove  whether  or  not  the  elec- 
trolyte can  be  spilled. 

0  This  requirement  will  be  met  by  lamps  that  have  an  angle  of  light 
stream  of  130°  or  more. 


MINE  LAMPS  AND  LIGHTING  323 

Tests  of  Design  and  Construction. — The  excellence  of  the  mechanical 
and  electrical  features  of  the  design  and  construction  of  the  lamps  will 
be  carefully  determined. 

The  following  tests  will  also  be  made:  Hand  lamps  and  the  head- 
pieces of  cap  lamps  will  be  dropped  10  times,  upon  a  concrete  floor 
from  a  point  6  ft.  above  it.  As  the  result  of  these  dropping  tests,  there 
must  be  no  breakage  of  the  battery  jar  or  material  distortion  of  the 
casing  of  the  battery  or  of  the  shell  of  the  headpiece.  The  engineers 
in  charge  of  the  investigation  shall  be  the  sole  judges  of  whether  or 
not  material  distortion  occurs.  The  dropping  tests  of  the  headpiece 
must  demonstrate  that  the  safety  devices  will  not  operate  unnecessarily. 

Cap  lamps  will  be  dropped  10  times,  upon  a  wooden  floor,  from  a 
point  3  ft.  above  it.  There  must  be  no  breakage  of  the  battery  jar 
or  material  distortion  of  the  casing. 

Tests  of  Safety  Devices. — In  making  tests  of  the  safety  devices,  it 
will  be  assumed  that  if  the  short-circuit  current  of  the  battery  does  not 
exceed  a  certain  value,  stated  previously,  the  glowing  filament  of  the 
lamp  is  the  only  source  of  danger. 

It  will  also  be  assumed  (based  on  tests  reported  in  Technical  Paper 
23)  that  the  glowing  filament  presents  an  element  of  danger,  in  the 
presence  of  mine  gas,  if  the  bulb  of  the  lamp  can  be  broken  without 
causing  the  filament  to  become  wholly  or  practically  extinguished  as 
the  result  of  the  action  of  the  safety  devices  with  which  the  lamp  is 
provided. 

The  tests  will  therefore  be  made  with  a  view  to  determining  whether 
or  not  the  lamp  bulb  may  be  broken  without  causing  the  safety  device 
of  the  lamp  to  extinguish  the  lamp  or  cause  the  filament  to  glow  at  a 
temperature  that  is  not  high  enough  to  ignite  explosive  mixtures  of  mine 
gas  and  air. 

If  the  safety  devices  are  designed  to  extinguish  the  lamp  before 
the  bulb  is  broken  it  will  not  be  necessary  to  make  the  tests  in  gas, 
unless  the  safety  devices  do  not  completely  extinguish  the  lamp.  It 
will  then  be  necessary  to  determine  whether  or  not  the  filament  is  glow- 
ing at  a  temperature  sufficient  to  ignite  gas. 

If  t-he  safety  devices  are  designed  to  extinguish  the  lamp  at  the  same 
time  that  the  bulb  is  broken  it  will  be  desirable  to  make  the  tests  in 
explosive  mixtures  of  gas  and  air. 

Gas,  if  used,  will  be  the  natural  gas  supplied  to  the  city  of  Pitts- 
burgh. The  composition  of  this  gas,  as  determined  from  recent  analyses, 
is  approximately  83.1  per  cent,  methane,  16  per  cent,  ethane,  0.9  per 
cent,  nitrogen  and  a  trace  of  carbon  dioxide. 

The  details  of  conducting  the  tests  will,  manifestly,  not  be  the  same 
for  all  lamps  submitted,  because  different  lamps  will  no  doubt  have 
safety  devices  differing  in  design,  construction  and  basic  principles. 
The  bureau  proposes  to  determine,  for  each  lamp  separately,  a  schedule 
of  tests  that,  after  due  examination  of  the  lamp  and  its  safety  devices, 


324  MINE  GASES  AND  VENTILATION 

seem  best  adapted  to  ascertaining  the  merits  of  the  equipment  sub- 
mitted. This  schedule  may  be  examined  and  discussed  by  the  manu- 
facturer's representative  before  the  tests  are  begun. 

In  general,  the  tests  will  consist  of  striking  the  mounting  or  holder 
of  the  lamp  bulb,  in  an  attempt  to  break  the  bulb  without  extinguish- 
ing the  lamp. 

If  the  safety  devices  are  designed  to  extinguish  the  lamp  (as,  by 
disconnecting  the  bulb  from  circuit,  or  by  opening  the  circuit  at  some 
other  point)  the  devices  will  be  considered  to  have  acted: 

1.  If,  after  the  blow  has  been  delivered,  the  lamp  bulb,  whether 
broken  or  not,  is  clearly  disconnected  from  circuit. 

2.  If,  after  the  blow  has  been  delivered: 

(a)  When  the  lamp  filament  is  not  broken  by  the  blow  and  does  not 
glow; 

(6)  When  the  lamp  filament  is  broken  by  the  blow  a  sound  filament, 
replacing  the  broken  filament,  does  not  glow. 

If  the  safety  devices  are  designed  to  decrease  the  temperature  of 
the  filament  (by  short-circuiting  the  filament  or  by  other  means), 
the  devices  will  be  considered  to  have  acted  if,  after  the  blow  has  been 
delivered: 

(a)  When  the  lamp  filament  is  not  broken  by  the  blow  it  does  not 
glow  at  a  temperature  sufficient  to  ignite  gas; 

(b)  When  the  lamp  filament  is  broken  by  the  blow  a  sound  fila- 
ment, replacing  the  broken  filament,  does  not  glow  at  a  temperature 
sufficient  to  ignite  gas. 

If  there  is  any  question  as  to  whether  or  not  a  filament  is  glowing 
at  a  dangerous  temperature  the  point  will  be  settled  by  surrounding 
the  filament  with  an  explosive  mixture  of  gas  and  air. 

If,  after  the  blow  has  been  delivered,  the  bulb  has  not  been  broken 
and  the  safety  devices  have  not  acted  the  test  will  be  repeated  with 
the  same  equipment,  or  with  a  different  equipment,  at  the  discretion 
of  the  bureau's  engineers. 

The  bureau  believes  that  approximately  50  tests  will  be  necessary 
to  determine  whether  or  not  the  safety  devices  of  a  lamp  are  permis- 
sible for  use  in  gaseous  mines;  but  more  or  fewer  tests  may  be  made 
at  the  discretion  of  the  engineer  in  charge  of  the  tests. 

To  Determine  Maximum  Short-circuit  Current. — The  short-circuit 
current  of  the  battery  will  be  measured  under  conditions  that  will  give 
the  same  current  that  would  flow  through  a  short-circuit  between  the 
conductors  of  the  flexible  cord,  at  the  point  in  the  cord  nearest  to  the 
battery  casing. 

Tests  of  Lighting. — The  tests  to  determine  the  time  of  burning,  flux, 
intensity  and  distribution  of  light  will  be  made,  for  not  less  than  20 
batteries,  6  reflectors  or  lamp  mountings,  and  100  lamp  bulbs. 

The  average  performance  of  the  various  equipments  will  be  taken 
as  the  average  performance  of  the  lamp.  The  measurements  of  flux 


MINE  LAMPS  AND  LIGHTING  325 

and  intensity  of  light  will  be  made  after  the  bulbs  have  been  burned 
for  about  10  hours  in  order  to  season  them  somewhat. 

Tests  of  Current  Consumption,  Candlepower,  Life  of  Bulb. — Mea- 
surements of  current  consumption  and  candlepower  will  be  made  with 
bulbs  that  have  been  burned  about  10  hours. 

Measurements  of  current  consumption  will  be  made  at  approxi- 
mately'the  average  potential  given  by  the  lamp  battery,  after  having 
been  used  for  one  hour. 

Measurements  of  bulb  candlepower  will  be  made  in  one  direction 
only.  Usually  the  direction  that  gives  the  largest  exposure  of  filament 
will  be  selected. 

Determination  of  bulb-life  will  be  made  with  batteries  that  have 
the  same  voltage  characteristics  as  those  used  with  the  lamp.  Tests 
will  be  made  with  the  bulbs  in  a  fixed  position. 

Although,  as  stated  in  Technical  Paper  75,  Bureau  of  Mines,  the 
bureau  considers  that  the  batteries  of  portable  electric  mine  lamps 
should  give  3600  hours  of  service  (300  12-hour  shifts)  without  requiring 
repairs  or  replacements  of  any  part,  it  is  manifestly  impracticable  for 
the  bureau  to  carry  out  the  3600-hour  test  upon  each  battery  submitted 
for  approval.  Therefore,  the  requirements  of  the  bureau,  with  respect 
to  the  durability  of  batteries,  will  be  considered  as  satisfied  if  the  batteries 
shall  perform  their  functions  without  repair  while  being  used  by  the 
bureau,  in  accordance  with  the  written  instructions  of  the  lamp  manu- 
facturer, to  conduct  the  bulb-life  tests;  and,  at  the  completion  of  these 
tests,  the  condition  of  the  batteries  shall  give  no  evidence  of  weakness 
that  indicates  the  early  failure  of  any  part  of  the  battery. 

Test  of  Leakage  of  Electrolyte. — The  lamps  will  be  tested  for  leakage 
and  spilling  of  electrolyte,  by  placing  the  batteries  for  various  lengths  of 
time,  totaling  eight  hours,  in  various  positions  that  seem  most  likely  to 
cause  the  cells  to  leak  or  spill.  If  a  battery  does  not  leak  or  spill  more 
than  one  full  drop  of  electrolyte  during  the  eight-hour  test  the  battery 
casing  will  be  regarded  as  non-spilling. 

Approval  of  Electric  Mine  Lamps. — The  manufacturers  will  bo  re- 
quired to  attach  to  the  battery  casing  of  each  permissible  lamp  equip- 
ment a  plate  bearing  the  seal  of  the  Bureau  of  Mines  and  inscribed  as 
follows: 

PERMISSIBLE  PORTABLE  ELECTRIC  MINE  LAMP.     APPROVAL  No. — . 

Issued  for  safety  and  for  practicability  and  efficiency  in  general 
service  to  the Co. 

The  use  of  the  plate  will  not  be  required  if  the  same  inscription  is 
stamped  or  cast  into  the  casing  of  the  battery. 

Manufacturers  shall,  before  claiming  the  bureau's  approval  for  any 
modification  of  any  approved  lamp,  submit  to  the  bureau  drawings 


326  MINE  GASES  AND  VENTILATION 

that  shall  show  the  extent  and  nature  of  such  modifications,  in  order 
that  the  bureau  may  decide  whether  or  not  it  should  test  the  remodeled 
lamp  before  approving  it.  Each  approval  of  a  permissible  lamp  will 
be  given  a  serial  number.  Approvals  of  modified  forms  of  a  previously 
approved  lamp  will  bear  the  same  number  as  the  original  approval 
with  the  addition  of  the  letters  a,  6,  c,  etc. 

The  bureau  will,  upon  request,  make  tests  of  lamp  bulbs  to  deter- 
mine whether  or  not  they  will  comply  with  the  bureau's  requirements 
when  used  in  connection  with  any  lamp  that  has  been  approved  by 
the  bureau  under  the  provisions  of  this  schedule.  Lamp  bulbs  that  fulfill 
the  requirements  will  be  specifically  approved  for  use  with  stated  lamps. 
Applications  for  tests  of  bulbs  should  be  made  in  a  manner  similar  to 
application  for  tests  of  lamps. 

The  bureau's  approval  of  any  lamp  shall  be  construed  as  applying 
to  all  lamps  made  by  the  same  manufacturer  that  have  the  same  con- 
struction in  the  details  considered  by  the  bureau,  but  to  no  other  lamps. 
The  bureau  reserves  the  right  to  rescind,  for  cause,  at  any  time,  any 
approval  granted  under  the  conditions  herein  set  forth. 

Notification  of  Manufacturer. — As  soon  as  the  bureau's  engineers  are 
satisfied  that  a  lamp  is  permissible,  the  manufacturer  of  the  lamp  and 
the  mine-inspection  departments  of  the  several  states  shall  be  notified 
to  that  effect.  As  soon  as  a  manufacturer  receives  formal  notification 
that  his  lamp  has  passed  the  tests  prescribed  by  the  bureau,  he  shall  be 
free  to  advertise  such  lamp  as  permissible.  <• 

Fees  for  Testing. — The  necessary  expenses  involved  in  testing  portable 
electric  mine  lamps  have  been  determined,  and  the  following  schedule 
of  fees  to  be  charged,  on  and  after  the  date  of  issue  of  this  schedule,  has 
been  established  and  approved  by  the  Secretary  of  the  Interior : 

1.  For  a  complete  official  investigation  leading  to  the  formal  ap- 

proval of  a  portable  electric  mine  lamp,  the  investigation  to 
include  tests  of  the  safety  devices  and  the  determination  of 
the  time  of  burning,  flux  of  light,  intensity  of  light,  distri- 
bution of  light,  bulb  characteristics,  leakage  of  electrolyte, 
and  durability $150.00 

2.  For  tests  of  the  safety  devices  only $30 . 00 

For  additional  necessary  tests,  under  the  same  investigation 

(for  each  five  tests  or  fraction  thereof) $2 . 50 

3.  For  tests  to  determine  only  the  time  of  burning,  flux  of  light, 

intensity  of  light,  distribution  of  light,  bulb  characteristics, 

and  leakage  of  electrolyte $120. 00 

4.  For  tests  to  determine  only  bulb  life,  variation  in  bulb  candle- 

power  and  variation  in  bulb  current  consumption: 

If  such  tests  involve  making  discharge-voltage  determin- 
ations        $75.00 

If    such    tests  do  not  involve  making  discharge-voltage 
determinations —  $50.00 


MINE  LAMPS  AND  LIGHTING  327 

5.  The  following  charges     will  be  made  for  individual  tests 

included  under  item  3: 

Discharge-voltage  tests $25 . 00 

Reflector  tests $20 . 00 

Time-of-burning  tests $10. 00 

Light-distribution  tests $5 . 00 

Electrolyte-spilling  tests $3 . 00 

Short-circuit  tests  of  battery $1 . 00 

Mechanical  tests  of  cord $6 . 00 

Bulb-life  tests $35 . 00 

Bulb-uniformity  tests $15 . 00 

0.  Special  tests  that  circumstances  shall  render  necessary,  during  the 

course  of  the  investigation,  will  be  made  at  the  request  of  the  lamp 

manufacturer  and  will  be  charged  for  in  accordance  with  the  amount 

of  work  involved. 


ADDENDA 

LOGARITHMS — CIRCULAR  FUNCTIONS,  SINES  AND  COSINES, 
TANGENTS  AND  COTANGENTS: — SQUARES,  CUBES,  ROOTS  AND 
RECIPROCALS  OF  NUMBERS — CIRCUMFERENCES  AND  AREAS — 
DENOMINATE  NUMBERS — WEIGHTS  AND  MEASURES — 
UNITED  STATES  AND  BRITISH  SYSTEMS — METRIC  SYSTEMS 
OF  WEIGHTS  AND  MEASURES — CONVERSION  TABLES — CON- 
VERSION OF  COMPOUND  UNITS. 

LOGARITHMS 

The  treatment  of  logarithms  here  will  be  simple  and  practical  and  such 
as  to  enable  their  use  to  be  clearly  understood.  Much  time  and  labor 
are  saved  when  multiplying  and  dividing,  or  when  extracting  the  roots 
of  numbers,  or  raising  a  number  to  a  given  power  by  the  use  of  loga- 
rithms. 

Definition. — The  logarithm  of  a  number  is  the  exponent  of  the  power 
to  which  it  is  necessary  to  raise  a  fixed  number  called  the  "base"  to 
produce  the  given  number. 

Systems  of  Logarithms. — There  are  two  systems  of  logarithms  in  use: 
1.  The  Briggs  or  common  system  employs  10  as  a  base.  2.  The  Na- 
perian  or  hyperbolic  or  natural  system  is  derived  from  2.71828+  as  a 
base.  The  common  logarithms  (log)  are  those  generally  used,  while  the 
natural  logarithms  (nat.  log)  are  often  employed  in  theoretical  analyses. 

The  Naperian  or  natural  logarithm  of  a  number  can  always  be  found 
by  multiplying  the  common  logarithm  of  the  number  by  2.302585,  which 
is  expressed  thus: 

Nat.  log.  =  2.302585  com.  log. 

In  any  system  of  logarithms,  the  logarithm  of  1  is  zero,  and  the  loga- 
rithm of  the  base  of  the  system  is  always  1. 

The  Logarithm. — Every  logarithm  is  composed  of  two  distinct  parts 
separated  by  a  decimal  point  The  number  preceding  the  decimal 
point,  or  the  integer  of  the  logarithm  is  called  the  characteristic,"  while 
the  decimal  portion  of  the  logarithm  is  the  "mantissa."  These  two  parts 
of  a  logarithm  must  be  regarded  separately.  The  mantissa  is  always  posi- 
tive, but  the  characteristic  may  be  either  positive  or  negative,  according 
as  the  given  number  is  greater  or  less  than  1,  in  a  system  whose  base  is 
greater  than  1. 

The  characteristic  is  always  1  less  than  the  number  of  figures  in  the 
integral  portion  of  the  given  number;  or  1  greater  than  the  number  of 
ciphers  following  the  decimal  point  when  the  given  number  is  wholly 

328 


ADDENDA  329 

decimal.     In  the  former  case  the  characteristic  is  positive;  in  the  latter 
case  it  is  negative.     The  following  examples  will  make  this  clear : 

log  325.00  =  2.51188  log  0.325       =  1.51188 

log    32.50  =  1.51188  log  0.0325     =2.51188 

log      3.25  =  0.51188  log  0.00325  =  3.51188 

The  mantissa,  as  is  readily  observed  from  the  above  examples,  is 
determined  by  the  sensible  figures  of  a  number,  without  regard  to  the 
decimal  point.  Also,  the  mantissa  of  the  logarithm  of  a  number  is 
unchanged  when  the  number  is  multiplied  or  divided  by  10,  100,  1,000, 
etc.  For  example,  the  mantissa  of  the  logarithm  of  3,  which  is  0.47712, 
is  the  same  for  30,  300,  3,000  or  for  0.3,  0.03,  0.003,  etc. 

A  table  of  the  common  logarithms  of  numbers  from  Oto  10, 000  follows 
and  will  be  found  useful.  In  this  table  the  mantissas  only  are  given  and, 
to  avoid  unnecessary  repetition,  the  first  two  figures  are  not  repeated. 
An  asterisk  *  appearing  before  the  remaining  three  figures  of  the  mantissa 
indicates  that  the  first  two  figures  must  be  taken  from  the  line  below. 
Bars  are  employed  to  mark  the  division  by  tens,  which  facilitates  the 
finding  of  the  mantissa  of  any  desired  number  given  in  the  left-hand 
column.  In  this  table,  the  differences  are  given  as  proportion  parts  and 
placed  in  the  right-hand  column  marked  "  P.  P.,"  which  avoids  the 
necessity  of  multiplying  by  the  decimal  as  will  be  explained. 

To  Find  the  Logarithm  of  a  Number. — From  the  table  of  logarithms, 
find  the  mantissa  corresponding  to  the  given  number,  ignoring  the  decimal 
point.  To  do  this,  the  first  three  figures  on  the  left  of  the  given  number 
are  found  in  the  left-hand  column  of  the  table,  and  the  fourth  figure  in 
the  line  at  the  top.  The  required  mantissa  is  then  taken  from  the  line 
and  column  thus  indicated. 

But  if  the  given  number  contains  five  or  more  figures,  write  the  excess 
figures  as  a  decimal  and  multiply  the  difference  between  the  mantissa 
found  and  the  one  next  following  by  this  decimal;  point  off  and  add  the 
integral  portion  of  the  result  to  the  mantissa  already  found.  If  desired 
this  logarithm  can  be  extended  by  annexing  the  decimal  portion  of  the 
same  result,  but  this  is  not  commonly  necessary.  When  there  is  but  one 
excess  figure,  as  when  finding  the  mantissa  of  a  number  having  five 
figures,  the  difference  to  be  added  to  complete  the  mantissa  is  taken 
from  the  corresponding  proportional  part,  in  the  right-hand  column  with- 
out multiplying. 

Having  found  the  mantissa,  prefix  a  decimal  point  preceded  by  a 
characteristic  one  less  than  the  number  of  integral  figures  in  the  given 
number.  If  there  is  but  one  integral  figure  the  characteristic  of  the 
logarithm  will  be  zero. 

If  the  given  number  is  a  decimal,  having  no  integral  figures,  the 
characteristic  will  be  negative  and  numerically  one  greater  than  the 
number  of  ciphers  that  follow  the  decimal  point. 


330  MINE  GASES  AND  VENTILATION 

Illustrations. — The  following  examples  will  illustrate  the  method 
of  finding  the  logarithms  of  numbers  under  different  conditions  and  make 
clear  the  use  of  the  table. 

1.  Suppose  it  is  required  to  find  the  logarithm  of  the  number  4,657. 
Opposite  465,  in  the  column  under  7,  is  found  811,  and  this  annexed  to 
66  found  at  the  left  gives  for  the  mantissa  of  this  number  the  decimal 
0.66811.     The  characteristic,   in  this  case,  is  3,   since  there  are  four 
integral  figures  in  the  given  number.     Hence,  log  4,657  =  3.66811. 

2.  To  find  the  logarithm  of  32.567,  ignoring  the  decimal  point,  opposite 
325  in  the  column  under  6,  is  found  the  mantissa,  0.51268;  but  there  is 
still  another  figure  7  in  the  given  number.     Therefore,  to  complete  this 
mantissa  subtract  it  from  the  one  following,  giving  the  difference   14 
found  in  the  right-hand  column.     The  proportional  part  of  this  difference 
corresponding  to  the  fifth  figure  7  is  9.8  or,  say  10.     Then  51,268  +  10  = 
51,278  and  the  complete  mantissa  is  therefore  0.51278.     In  this  case, 
the  given  number  contains  but  two  integral  figures,  which  makes  the 
characteristic  1;  hence,  log  32.567  =  1.51278. 

3.  To  find  the  logarithm  of  0.509065,  ignoring  the  decimal  point, 
opposite   509,  in  the  column  under  0,  is  found  the  mantissa  0.70672. 
To  complete  this  mantissa   subtract  it  from  the  one  next  following, 
thus,  680  —  672  =  8,  and  multiply  the  remaining  figures  of  the  given 
number  written  as  a  decimal,  by  the  difference  8  and  add  the  integral 
of  the  result  to  the  mantissa  already  found. 

Thus,  70,672  +  0.65  X  8  =  70,672  +  5  =  70,677. 

Now,  since  the  given  number  is  a  decimal,  the  characteristic  of  its 
logarithm  is  negative;  and  its  numerical  value  is  1,  as  there  are  no  ciphers 
immediately  following  the  decimal  point.  The  complete  logarithm  is, 
therefore,  log  0.509065  =  1.70677,  the  minus  sign  being  written  over 
the  characteristic,  since  the  characteristic  only  is  negative. 

Use  of  Logarithms. — By  the  use  of  logarithms  the  processes  of  multi- 
plication, division,  involution  and  evolution  are  greatly  shortened  and 
simplified.  The  two  latter  processes  are  in  fact  a  repetition  of  the  two 
former;  while  division  and  evolution  are  the  reverse  operations  of  multi- 
plication and  involution,  respectively. 

It  is  important  to  observe  that  the  use  of  logarithms  enables  the  finding 
of  decimal  powers  and  decimal  roots  of  numbers,  which  is  impossible 
by  other  means.  When  the  index  of  a  power  or  root  of  a  number 
can  be  expressed  as  a  fraction  the  numerator  and  denominator  of  such 
fraction  express,  respectively,  the  indices  of  the  power  and  root  or  the  root 
and  power,  as  the  case  may  be.  A  decimal  index,  therefore,  expresses 
in  one  operation  the  extraction  of  any  given  root  of  any  given  power  of  a 
number,  which  will  be  better  understood  later. 

The  application  of  this  principle  is  shown  in  numerous  instances 
where  quantities  vary  in  their  relation  to  each  other  according  to  different 
powers.  For  example,  in  fan  ventilation,  the  fourth  power  of  the  speed 


ADDENDA  331 

(n4)  of  the  fan  varies  as  the  fifth  power  of  the  quantity  (qr°)  of  air  in  circula- 
tion ;  which  is  expressed  as  follows : 

n -4  varies  as  q5 

or  n  varies  as  q*;  or  r/'-25 

and  q  varies  as  n5;  or  n0-8 

The  expression  n«  or  the  fourth-fifths  power  of  n  is  identical  with 
V/rt4  or  the  fifth  root  of  the  fourth  power  of  n.  Hence,  to  extract  the 
root  of  a  power,  divide  the  exponent  of  the  power  by  the  index  of  the 
desired  root  and  the  quotient  will  be  the  new  exponent,  which  combines 
the  two  operations  in  a  single  transaction. 

Rules  for  the  Use  of  Logarithms. — The  following  four  simple  rules  cover 
all  the  operations  of  logarithms: 

1.  Multiplication :  To  find  the  product  of  two  or  more  numbers,  add 
their  logarithms;  the  number  corresponding  to  this  logarithmic  sum  is  the 
desired  product. 

In  other  words,  the  logarithm  of  the  product  of  two  or  more  numbers  is 
equal  to  the  sum  of  the  logarithms  of  the  numbers. 

2.  Division :  To  divide  one  number  by  another,  subtract  the  logarithm 
of  the  divisor  from  that  of  the  dividend;  the  number  corresponding  to 
this  logarithmic  remainder  is  the  required  quotient. 

In  other  words,  the  logarithm  of  the  quotient  is  equal  to  the  logarithm 
of  the  dividend  minus  that  of  the  divisor. 

3.  Involution:    To  find  any  given  power  of  a  number,  multiply  the 
logarithm  of  the  number  by  the  exponent  of  the  power;  the  number  corre- 
sponding to  the  resulting  logarithm  is  the  required  power  of  the  given 
number. 

4.  Evolution :  To  find  any  given  root  of  a  number,  divide  the  logarithm 
of  the  number  by  the  index  of  the  root;  the  number  corresponding  to  the 
resulting  logarithm  is  the  required  root  of  the  given  number. 

Arithmetical  Complement. — The  arithmetical  complement  of  a  loga- 
rithm is  the  remainder  found  by  subtracting  the  log  from  10;  the  logarithm 
of  3  is  0.47712,  and  its  arithmetical  complement  is,  therefore,  10  - 
0.47712  =  9.52288.  Its  use  involves  subtracting  from  the  final  result 
as  many  tens  as  have  thus  entered  the  solution.  The  antilog  is  more  con- 
venient for  use. 

The  Antilog. — The  solution  of  problems  frequently  involves  the 
multiplication  and  division  of  many  quantities.  In  the  use  of  logarithms, 
the  sum  of  the  logs  of  the  divisors  would  be  subtracted  from  the  sum  of 
the  logs  of  the  multipliers,  to  obtain  the  log  of  the  final  result.  By  the  use 
of  what  is  called  the  "antilog"  of  each  divisor,  it  is  possible  to  complete 
such  a  solution  in  a  single  operation,  by  adding  together  the  logs  of  the 
multipliers  and  the  antilogs  of  the  divisors. 

The  antilog  of  a  number  is  obtained  as  follows:  Subtract  the  mantissa 
of  its  log  from  1,  for  the  mantissa  of  the  antilog.  Then,  add  1  to  the 
characteristic  of  the  log  and  change  its  sign,  the  addition  being  always 
algebraic.  The  following  examples  will  make  the  process  understood: 


332  MINE  GASES  AND  VENTILATION 

1.  To  find  the  antilog  of  800:  Log  800  =  2.90309 
Mantissa  of  antilog,                     1  -  0.90309  =  0.09691 
Characteristic  of  antilog,             2  +  1  =3;  and  changing  sign  =  —  3 
Hence Antilog  800  =  3 . 09691 

2.  To  find  the  antilog  of  2:  log  2  =  0.30103 
Mantissa  of  antilog,                    •  1  -  0 . 30103  =  0 . 69897 
Characteristic  of  antilog,             0  +  1  =  1 ;  giving  -  1 

Hence Antilog      2  =  T. 69897 

3.  To  find  the  antilog  of  0.4:  Log  0.4  =  T .  60206 
Mantissa  of  antilog,                      1  —  0 . 60206  =  0 . 39794 
Characteristic  of  antilog,              —1+1=0  (zero  has  no  sign) 

Hence Antilog  0.4  =  0.39794 

4.  To  find  the  antilog  of  0.00125:  Log  0.00125   =  3.09691 
Mantissa  of  antilog,                     1  -  0.09691  =  0.90309 
Characteristic  of  antilog,              —3  +  1  =   —  2;  giving  +  2 

Hence Antilog  0.00125  =2.90309 

Note. — The  use  of  the  antilog  accomplishes  the  same  purpose  as  the 
arithmetical  complement  and  requires  no  correction  of  the  final  result  as 
explained  in  reference  to  the  latter.  It  should  be  observed  that  the 
antilog  of  a  number  is  always  the  log  of  the  reciprocal  of  that  number. 
Thus,  Log  800  =  antilog  1/800  or  0.00125 

As    shown    above,    log    800  =  2.90309;    antilog    0.00125  =  2.90309. 
Example. — Solve  the  following  by  the  use  of  logarithms: 

_  ksq2   _  0.00000002  X  40,000  X  50,0002 

a3  ~   503 

Solution.—  log  0.00000002 ,  8.30103 

log  40,000 4 . 60206 

log  50,0002  (4.69897  X  2) 9.39794 

antilog  503,       (log  503  =  1.69897  X  3  =  5.09691) 6.90309 

Log  p 1.20412 

Hence  p  =  16  Ib.  per  sq.  ft. 


LOGARITHMIC  TABLES 


COMMON  LOGARITHMS  OF  NUMBERS 


No. 

Log. 

No. 

Log. 

NO. 

Log. 

No. 

Log. 

NO. 

Log. 

0 

—  00 

20 

30  103 

40 

60206 

60 

77  815 

80 

90  309- 

l 

00  000 

21 

32222 

41 

61  278 

61 

78  533 

81 

90849 

2 

30  103 

22 

34  242 

42 

62  325 

62 

79  239 

82 

91  381 

8 

47712 

23 

36  173 

43 

63  347 

63 

79  934 

83 

91  908 

4 

60  206 

24 

38  021 

44 

64  345 

64 

80  618 

84 

92428 

5 

69897 

2-5 

39  794 

45 

65  321 

65 

81  291 

85 

92  942 

6 

77  815 

26 

41  497 

4fi 

66  276 

66 

81  954 

86 

93  450 

7 

84  510 

27 

43  136 

47 

67  210 

67 

82  607 

87 

93952 

8 

90  309 

28 

44  716 

48 

68  124 

68 

83  251 

88 

94  448 

9 

95  424 

29 

46  240 

49 

69020 

69 

83  885 

89 

94  939 

10 

00000 

30 

47712 

50 

69  897  • 

70 

84.510 

90 

95  424 

11 

04  139 

31 

49  136 

51 

70  757 

71 

85  126 

91 

95904 

12 

07  918 

32 

50  515 

5?, 

71  600 

72 

85  733 

92 

%  379 

13 

11  394 

33 

51  851 

53 

72  428 

73 

86  332 

93 

96848 

14 

14  613 

34 

53  148 

54 

73  239 

74 

86  923 

94 

97  313 

15 

17  609 

35 

54  407 

55 

74  036 

75 

87506 

95 

97  772 

16 

20412 

36 

55  630 

56 

74  819 

76 

88081 

96 

98  227 

17 

23  045 

37 

56820 

57 

75  587 

77 

88  649 

97 

98  677 

18 

,25  527 

38 

57  978 

58 

76  343 

78 

89  209 

98 

99  123 

19 

27  875 

39 

59106 

59 

77  085 

79 

89  763 

99 

99  564 

20 

30103 

40 

60206 

60 

77815 

80 

90309 

100 

00000 

333 


334 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

too 

101 
102 
103 
104 
105 
106 
107 
108 
109 

110 

111 

112 
113 
114 
115 
116 
117 
118 
119 

120 

121 
122 
123 
124 
125 
126 
127 
128 
129 

130 

131 

132 
133 
134 
135 
136 
137 
138 
139 

140 

141 
142 
143 
144 
145 
146 
147 
148 
149 

ISO 

00000 

043 

087 

130 

173 

604 
*030 
452 
870 
284 
694 
*100 
503 
902 

217 

647 
*072 
494 
912 
325 
735 
*141 
543 
941 

260 

689 
*115 
536 
953 
366 
776 
*181 
583 
981 

376 

303 

732 
*157 
578 
995 
407 
816 
*222 
623 
*021 

415 

346 

775 
*199 
620 
*036 
449 
857 
*262 
663 
*060 

454 

389 

c 
7 
8 
1 

1 
2 

3 
4 
5 
G 

7 

8 

y 

i 

•i 

3 
4 
5 
6 

7 

8 

g 

a 
a 

4 
5 

0 

7 
8 
9 

44 

4.4 

8.8 
13.2 
17.6 
22.0 
26.4 
30.8 
35.2 
39.6 

41 

4.1 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 

38 

8.8 
7.G 
11.4 
15.2 
19.0 
22.8 
26.6 
30.4 
34.2 

35 

8.5 

7.0 
10.5 
14.0 
17.5 
21.0 
24.5 
28.0 
31.5 

32 

3.2 
6.4 
9.6 
12.8 
16.0 
192 
22.4 
25.6 
28.8 

43 

4.3 

8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 

40 

4.0 

8.0 
12.0 
16.0 
20.0 
24.0 
28.0 
32.0 
36.0 

37 

8.7 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
296 
33.3 

34 

3.4 
6.8 
10.2 
13.6 
17.0 
20.4 
23.8 
27.2 
30.6 

31 

3.1 

6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

42 

4.2 

8.4 
12.6 
16.8 
21.0 
25.2 
29.4 
33.6 
37.8 

39 

3.9 
7.8 
11.7 
15.6 
19.5 
23.4 
27.3 
31.2 
33.1 

33 

3.6 

7.2 
10.8 
14.4 
18.0 
21.6 
25.2 
28.8 
32.4 

33 

3.3 
6.6 
9.9 
13.2 
16.5 
19.8 
23.1 
26.4 
29.7 

'30 

3.0 
6.0 
9.0 
12.0 
15.0 
18.0 
21.0 
24.0 
27.0 

432 
860 
01  284 
703 
02  119 
531 
938 
03  342 
743 

04  139 

475 
903 
326 
745 
160 
572 
979 
383 
782 

518 
945 
368 
787 
202 
612 
*019 
423 
822 

561 
988 
410 
828 
243 
653 
*060 
463 
862 

817 
*242 
662 
*078 
490 
898 
*302 
703 
*100 

179 

571 
961 
346 
729 
108 
483 
856 
225 
591 

218 

258 

650 
*038 
423 
805 
183 
558 
930 
298 
664 

297 

336 

493 

532 
922 
05  308 
690 
06  070 
446 
819 
07  188 
555 

610 
999 
385 
767 
145 
521 
893 
262 
628 

689 
*077 
461 
843 
221 
595 
967 
335 
700 

*063 

727 
*115 
500 
881 
258 
633 
*004 
372 
737 

*099 

458 
814 
*167 
517 
864 
209 
551 
890 
227 

5G1 

766 
*154 
538 
918 
296 
670 
*041 
408 
773 

*135 

805 
*192 
576 
956 
333 
707 
*078 
445 
809 

844 
*231 
614 
994 
371 
744 
*115 
482 
846 

*207 

883 
*2G9 
652 
*032 
408 
781 
*151 
518 
882 

*243 

918 

954 

990 

*027 

386 
743 
*096 
447 
795 
140 
483 
823 
160 

*171 

08279 
636 
991 
09  342 
691 
10037 
380 
721 
11  059 

314 

672 
*026 
377 
726 
072 
415 
755 
093 

350 
707 
*061 
412 
760 
106 
449 
789 
126 

422 
778 
*132 
482 
830 
175 
517 
857 
193 

528 

493 
849 
*202 
552 
899 
243 
585 
924 
261 

594 

529 
884 
*237 
587 
934 
278 
619 
958 
294 

565 
920 
*272 
621 
968 
312 
653 
992 
327 

600 
955 
*307 
656 
*003 
346 
687 
*025 
361 

694 

394 

428 

461 

494 

628 

661 

727 
12  057 
385 
710 
13  033 
354 
672 
988 
14  301 

760 
090 
418 
743 
066 
386 
704 
*019 
333 

644 

793 
123 
450 
775 
098 
418 
735 
*051 
364 

826 
156 
483 
808 
130 
450 
767 
*082 
395 

860 
189 
516 
840 
162 
481 
799 
*114 
426 

893 
222 
548 
872 
194 
513 
830 
*145 
457 

768 

926 
254 
581 
905 
226 
545 
862 
*176 
489 

959 
287 
613 
937 
258 
577 
893 
*208 
520 

992 
320 
646 
9G9 
290 
609 
925 
*239 
551 

*024 
352 
678 
*001 
322 
640 
956 
*270 
582 

613 

675 

706 

*014 
320 
625 
927 
227 
524 
820 
114 
406 

737 

799 

*106 
412 
715 
*017 
316 
613 
909 
202 
493 

829 

*137 
412 
746 
*047 
346 
643 
938 
231 
522 

860 

891 

922 
15229 
534 
836 
16  137 
435 
732 
17  026 
319 

953 
259 
564 
866 
167 
465 
761 
056 
348 

983 
290 
594 
897 
197 
495 
791 
085 
377 

*045 
351 
655 
957 
256 
554 
850 
143 
435 

*076 
381 
685 
987 
286 
584 
879 
173 
464 

*168 
473 
776 
*077 
376 
673 
967 
260 
551 

*198 
503 
806 
*107 
406 
702 
997 
289 
580 

1 
•1 

9 

609 

638 
1 

667 

696 

725 

754 

782 

811 

840 

869 

N. 

L.O 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


335 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.] 

> 

150 

17  609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

151 
152 
153 
154 
155 
156 
157 
158 
159 

898 
18  184 
469 
752 
19  033 
312 
590 
866 
20  140 

926 
213 
498 
780 
061 
340 
618 
893 
167 

955 
241 
526 
808 
089 
368 
645 
921 
194 

984 
270 
554 
837 
117 
396 
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327 
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173 
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355 
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29 

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28 

2.8 
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19.6 
22.4 
25.2 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

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161 
162 
163 
164 
165 
166 
167 
168 
169 

683 
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21  219 
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978 
245 
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298 
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737 
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324 
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299 
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350 
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115 
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141 
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220 
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925 

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2.6 
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170 

23  045 

070 

096 

121 

147 

172 

198 

223 

249 

274 

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172 
173 
174 
175 
176 
177 
178 
179 

300 
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25  042 
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325 
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830 
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329 
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310 

350 
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105 
353 
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334 

376 
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401 
654 
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155 
403 
650 
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139 
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426 
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180 
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2 
3 
4 
5 
6 
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24 

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16.8 
19.2 
21.6 

23 

2.3 
4.6 
6.9 
9.2 
11.5 
13.8 
16.1 
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20.7 

190 

875 

898 

921 

944 

967 

989 

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191 
192 
193 
194 
195 
196 
197 
198 
199 

28  103 
330 
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29  003 
226 
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126 
353 
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248 
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149 

375 
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194 
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314 
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217 
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240 
466 
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137 
358 
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262 
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713 
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159 
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285 
511 
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181 
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307 
533 
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203 
425 
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1 
2 
3 

4 
5 
6 
7 
8 
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22 

2.2 
4.4 

6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 

21 

2.1 
4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
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200 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

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L.O 

1 

2 

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4 

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336 


MINE  GASES  AND  VENTILATION 


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1 

2 

3 

4 

5 

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7 

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200 

30  103 

125 

146 

168 

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298 

201 
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204 
205 
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207 
208 
209 

320 
535 
750 
963 
31  175 
387 
597 
806 
32  015 

341 

557 
771 

984 
197 
408 
618 
827 
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363 
578 
792 
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218 
429 
639 
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384 
600 
814 
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239 
450 
660 
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406 
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260 
471 
681 
890 
098 

428 
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281 
492 
702 
911 
118 

449 
664 
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302 
513 
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139 

471 
685 
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534 
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160 

492 
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514 
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201 

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4 
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0 

2 
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21 

2.1 
4.2 
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210 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 

211 
212 
213 
214 
215 
216 
217 
218 
219 

428 
634 
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33  041 
244 
445 
646 
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449 
654 
858 
062 
264 
465 
666 
866 
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082 
284 
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084 

490 
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102 
304 
506 
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104 

510 
715 
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122 
325 
526 
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925 
124 

531 
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143 
345 
546 
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552 
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163 
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220 

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246 
247 
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238 
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256 
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292 
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346 
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364 
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LOGARITHMIC  TABLES 


337 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

250 

251 
252 
253 
254 
255 
256 
257 
258 
259 

260 

261 
262 
263 
264 
265 
266 
267 
268 
269 

270 

-271 
272 
273 
274 
275 
276 
277 
278 
279 

280 

281 
282 
283 
284 
285 
286 
287 
288 
289 

290 

291 
292 
293 
294 
295 
296 
297 
298 
299 

300 

39794 

811 

829 

846 

863 

881 

898 

915 

933 

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8 
9 

1 

8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

18 

1.8 
8.6 

5.4 
7.2 
9.0 
10.8 
12.6 
14.4 
16.2 

17 

1.7 
3.4 
5.1 
6.8 
8.5 
10.2 
11.9 
13.6 
15.S 

16 

1.6 
3.2 
4.8 
6.4 
8.0 
9.6 
11.2 
12.8 
14.4 

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1.5 
3.0 
4.5 
6.0 
7.5 
9.0 
10.5 
12.0 
13.5 

14 

1.4 
28 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 

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40  140 
312 
483 
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41  162 
330 

985 
157 
329 
500 
671 
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179 
347 

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175 
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518 
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192 
364 
535 
705 
875 
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212 
380 

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209 
381 
552 
722 
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229 
397 

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226 
398 
569 
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246 
414 

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243 
415 
586 
756 
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261 
432 
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296 
464 

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295 
466 
637 
807 
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313 
481 

497 

514 

531 

547 

564 

581 

597 

614 

631 

647 

664 
830 
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42  160 
325 
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681 
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177 
341 
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697 
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357 
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406 
570 
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217 

377 

537 
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170 
326 
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638 

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423 
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780 
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765 
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814 
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308 
472 
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43  136 

152 

169 

185 

201 

361 
521 
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154 
311 
467 
623 

233 

393 
553 
712 
870 
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185 
342 
498 
654 

249 

409 
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727 
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358 
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265 

425 
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217 
373 
529 
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281 

441 
600 
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232 
389 
545 
700 

297 
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616 
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44  091 
248 
404 
560 

313 
473 
632 
791 
949 
107 
264 
420 
576 

329 

489 
648 
807 
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122 
279 
436 
592 

345 

505 
664 
823 
981 
138 
295 
451 
607 

716 

731 

747 

762 

778 

793 

809 

824 

840 

855 

871 
45  025 
179 
332 
484 
637 
788 
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040 
194 
347 
500 
652 
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105 

902 
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209 
362 
515 
667 
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969 
120 

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225 
378 
530 
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135 

932 
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240 
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948 

102 
255 
408 
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864 
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165 

963 
117 
271 
423 
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728 
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133 
286 
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195 

994 
148 
301 
454 
606 
758 
909 
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210 

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163 
317 
469 
621 
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924 
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225 

240 

255 

270 

285 

434 
583 
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173 
319 
465 
611 

300 

315 

330 

345 

494 
642 
790 
938 
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232 
378 
524 
669 

359 

374 

389 
538 
687 
835 
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47  129 
276 
422 
567 

404 
553 
702 
850 
997 
144 
290 
436 
582 

419 
568 
716 
864 
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159 
305 
451 
596 

449 
598 
746 
894 
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188 
334 
480 
625 

464 
613 
761 
909 
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202 
349 
494 
640 

479 
627 
776 
923 
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217 
363 
509 
654 

509 
657 
805 
953 
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246 
392 
538 
683 

523 
672 
820 
967 
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261 
407 
553 
698 

712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

338 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

756 

900 
044 
187 
330 
473 
615 
756 
897 
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4 

5 

6 

799 

943 

087 
230 
373 
515 
657 
799 
940 
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7 

813 

958 
101 
244 
387 
530 
671 
813 
954 
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8 

9 

P.P. 

300 

301 
302 
303 
304 
305 
306 
307 
308 
309 

310 

311 
312 
313 
314 
315 
316 
317 
318 
319 

320 

321 

322 
323 
324 
325 
326 
327 
328 
329 

330 

331 
332 
333 
334 
335 
336 
337 
338 
339 

340 

47  712 

727 

871 
015 
159 
302 
444 
586 
728 
869 
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741 

885 
029 
173 
316 
458 
601 
742 
883 
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770 

784 

828 

842 

986 
130 
273 
416 

558 
700 
841 
982 
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262 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

15 

1.5 

3.0 
4.5 
6.0 
7.5 
9.0 
10.5 
12.0 
13.5 

14 

1.4 
2.8 
4.2 
5.8 
7.0 
8.4 
9.8 
11.2 
12.6 

13 

1.3 

2.6 
3.9 
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6.5 
7.8 
9.1 
10.4 
11.7 

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1.2 
2.4 
3.6 
4.8 
6.0 
7.2 
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9.6 
10.8 

857 
48  001 
144 
287 
430 
572 
714 
855 
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914 
058 
202 
344 
487 
629 
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911 
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929 
073 
216 
359 
501 
643 
785 
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972 
116 
259 
401 
544 
686 
827 
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49  136 

150 

290 
429 
568 
707 
845 
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120 
256 
393 

164 

178 

192 

332 
471 
610 
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161 
297 
433 

206 

346 

485 
624 
762 
900 
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174 
311 
447 

220 

234 

248 

276 
415 
554 
693 
831 
969 
50  106 
243 
379 

304 
443 
582 
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133 
270 
406 

318 
457 
596 
734 
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147 
284 
420 

360 
499 
638 
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188 
325 
461 

374 
513 
651 
790 
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202 
338 
474 

388 
527 
665 
803 
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352 
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402 
541 
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817 
955 
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229 
365 
501 

515 

529 

542 

556 

691 
826 
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095 
228 
362 
495 
627 
759 

891 

569 

583 

596 

610 

745 
880 
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148 
282 
415 
548 
680 
812 

623 

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162 
295 
428 
561 
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825 

637 

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587 
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348 
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614 
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108 
242 
375 
508 
640 
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718 
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521 
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135 
268 
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534 
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621 
750 
879 
*007 
135 

851 

865 

996 
127 
257 
388 
517 
647 
776 
905 
033 

161 

878 

904 

917 

930 

*061 
192 
323 
453 
582 
711 
840 
969 
097 

224 

943 

*075 
205 
336 
466 
595 
724 
853 
982 
110 

957 

983 
o2  114 
244 
375 
504 
634 
763 
892 
53  020 

*009 
140 
270 
401 
530 
660 
789 
917 
046 

173 

*022 
153 
284 
414 
543 
673 
802 
930 
058 

186 

*035 
166 
297 
427 
556 
686 
815 
943 
071 

199 

*048 
179 
310 
440 
569 
699 
827 
956 
084 

212 

*088 
218 
349 
479 
608 
737 
866 
994 
122 

148 

237 

250 

263 

341 
342 
343 
344 
345 
346 
347 
348 
349 

350 

275 
403 
529 
656 
782 
908 
54033 
158 
283 

288 
415 
542 
668 
794 
920 
045 
170 
295 

301 
428 
555 
681 
807 
933 
058 
183 
307 

314 
441 
567 
694 
820 
945 
070 
195 
320 

326 
453 
580 
706 
832 
958 
083 
208 
332 

339 
466 
593 
719 
845 
970 
095 
220 
345 

352 
479 
605 
732 
857 
983 
108 
233 
357 

481 

364 
491 
618 
744 
870 
995 
120 
245 
370 

377 
504 
631 
757 
882 
*008 
133 
258 
382 

390 
517 
643 
769 
895 
*020 
145 
270 
394 

407 

419 

432 

444 

456 

469 

494 

506 
8 

518 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

9 

P.P. 

LOGARITHMIC  TABLES 


339 


N. 

L.O 

1 

2 

3 

4 

456 

580 
704 
827 
949 
072 
194 
315 
437 
558 

5 

6 

7 

8 

9 

P.P. 

350 

351 
352 
353 
354 
355 
356 
357 
358 
359 

360 

361 
362 
363 
364 
365 
366 
367 
368 
369 

370 

371 
372 
373 
374 
375 
376 
377 
378 
379 

380 

381 

382 
383 
384 
385 
386 
387 
388 
389 

390 

391 

392 
393 
394 
395 
396 
397 
398 
399 

400 

54  407 

419 

432 

444 

469 

481 

494 

506 

518 

6 

7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

8 
9 

1 

8 
9 

13 

1.3 
2.6 
3.9 
5.2 
6.5 
7.8 
9.1 
10.4 
11,7 

12 

1.2 
2.4 
3.6 
4.8 
6.0 
7.2 
8.4 
9.6 
10.8 

II 

1.1 

2.2 
3.3 
4.4 
5.5 
6.6 
7.7 
8.8 
9.9 

10 

1.0 
2,0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 

531 
654 
777 
900 
55  023 
145 
267 
388 
509 

543 
667 
790 
913 
035 
157 
279 
400 
522 

555 
679 
802 
925 
047 
169 
291 
413 
534 

654 

568 
691 
814 
937 
060 
182 
303 
425 
546 

593 
716 
839 
962 
084 
206 
328 
449 
570 

605 
728 
851 
974 
096 
218 
340 
461 
582 

703 

823 
943 
*062 
182 
301 
419 
538 
656 
773 

617 
741 
864 
986 
108 
230 
352 
473 
594 

630 
753 
876 
998 
121 
242 
364 
485 
606 

727 

847 
967 
*086 
205 
324 
443 
561 
679 
797 

642 
765 
888 
*011 
133 
255 
376 
497 
618 

630 

642 

666 

678 

691 

715 

835 
955 
*074 
194 
312 
431 
549 
667 
785 

739 

859 
979 
*098 
217 
336 
455 
573 
691 
808 

751 
871 
991 
56  110 
229 
348 
467 
585 
703 

763 
883 
*003 
122 
241 
360 
478 
597 
714 

775 
895 
*015 
134 
253 
372 
490 
608 
726 

787 
907 
*027 
146 
265 
384 
502 
620 
738 

799 
919 
*038 
158 
277 
396 
514 
632 
750 

811 
931 
*050 
170 
289 
407 
526 
644 
761 

820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

937 
57  054 
171 
287 
403 
519 
634 
749 
864 

949 
066 
183 
299 
415 
530 
646 
761 
875 

961 

078 
194 
310 
426 
542 
657 
772 
887 

972 
089 
206 
322 
438 
553 
669 
784 
898 

*013 

984 
101 
217. 
334 
449 
565 
680 
795 
910 

996 
113 
229 
345 
461 
576 
692 
807 
921 

*008 
124 
241 
357 
473 
588 
703 
818 
933 

*019 
136 
252 
368 
484 
600 
715 
830 
944 

*058 

*031 
148 
264 
380 
496 
611 
726 
841 
955 

*043 
159 
276 
392 
507 
623 
738 
852 
967 

978 

990 

*001 

*024 

*035 

149 
263 
377 

490 
602 
715 
827 
939 
*051_ 

162 

*047 

*070 

*081 

58092 
206 
320 
433 
546 
659 
771 
883 
995 

104 
218 
331 
444 
557 
670 
782 
894 
*006 

115 
229 
343 
456 
569 
681 
794 
906 
*017 

127 
240 
354 
467 
580 
692 
805 
917 
*028 

138 

252 
365 
478 
591 
704 
816 
928 
*040 

161 

274 
388 
501 
614 
726 
838 
950 
*062 

173 

172 
286 
399 
512 
625 
737 
850 
961 
*073 

184 
297 
410 
524 
636 
749 
861 
973 
*084 

195 
309 
422 
535 
647 
760 
872 
984 
*095 

59  106 

218 
329 
439 
550 
660 
770 
879 
988 
60  097 

118 

129 

140 

151 

184 

195 

207 

229 
340 
450 
561 
671 
780 
890 
999 
108 

240 
351 
461 
572 
682 
791 
901 
*010 
119 

251 
362 
472 
583 
693 
802 
912 
*021 
130 

262 
373 
483 
594 
704 
813 
923 
*032 
141 

273 
384 
494 
605 
715 
824 
934 
*043 
152 

284 
395 
506 
616 
726 
835 
945 
*054 
163 

271 

295 
406 
517 
627 
737 
846 
956 
*065 
173 

306 
417 

528 
638 
748 
857 
966 
*076 
184 

318 
428 
539 
649 
759 
868 
977 
*086 
195 

304 

206 

217 

228 

239 

249 

260 

282 

293 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

340 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

Q 

9 

P.P. 

400 

60  206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

401 
402 
403 
404 
405 
406 
407 
408 
409 

314 
423 
531 
638 
746 
853 
959 
61  066 
172 

325 
433 
541 
643 
756 
863 
970 
077 
183 

336 
444 

552 
660 
767 
874 
981 
087 
194 

347 

455 
563 
670 
778 
885 
991 
098 
204 

358 
466 
574 
681 
788 
895 
*002 
109 
215 

369 
477 
584 
692 
799 
906 
*013 
119 
225 

379 
487 
595 
703 
810 
917 
*023 
130 
236 

390 
498 
606 
713 
821 
927 
*034 
140 
247 

401 
509 
617 
724 
831 
938 
*045 
151 
257 

412 

520 
627 
735 
842 
949 
*055 
162 
268 

II 

l.l 

2.2 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

i  *•* 

411 

412 
413 
414 
415 
416 
417 
418 
419 

384 
490 
595 
700 
805 
909 
62  014 
118 
221 

395 
500 
606 
711 
81'' 
920 
024 
128 
232 

405 
511 
616 
'.21 
826 
930 
034 
138 
242 

416 
521 
627 
731 
836 
941 
045 
149 
252 

426 
532 
637 
742 
847 
951 
055 
159 
263 

437 
542 
648 
752 
857 
962 
066 
170 
273 

448 
553 
658 
763 
868 
972 
076 
180 
284 

458 
563 
669 
773 
878 
982 
086 
190 
294 

469 
574 
679 
784 
888 
993 
097 
201 
304 

479 
584 
690 
794 
899 
*003 
107 
211 
315 

1  6.6 
7   7.7 
8   8.8 
9  9.9 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

421 
422 
423 
424 
425 
426 
427 
428 
429 

428 
531 
634 
737 
839 
941 
63  043 
144 
246 

439 
542 
644 
747 
849 
951 
053 
155 
256 

449 
552 
655 
757 
859 
961 
063 
165 
266 

459 
562 
665 
767 
870 
972 
073 
175 
276 

469 
572 
675 

778 
880 
982 
083 
185 
286 

480 
583 
685 
788 
890 
992 
094 
195 
296 

490 
593 
696 
798 
900 
*002 
104 
205 
306 

500 
603 
706 
808 
910 
*012 
114 
215 
317 

511 
613 
716 
818 
921 
*022 
124 
225 
327 

521 
624 
.726 
829 
931 
*033 
134 
236 
337 

1  1.1.0 
2   2.0 
3   3.0 
4  4.0 
5  5.0 
6  6.0 
7   7.0 
8   8.0 
9  .  9.0 

430 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 

431 
432 
433 
434 
435 
436 
437 
438 
439 

448 
548 
649 
749 
849 
949 
64048 
147 
246 

458 
558 
659 
759 
859 
959 
058 
157 
256 

468 
568 
669 
769 
869 
969 
068 
167 
266 

478 
579 
679 
779 
879 
979 
078 
177 
276 

488 
589 
689 
789 
889 
988 
088 
187 
286 

498 
599 
699 
799 
899 
998 
098 
197 
296 

508 
609 
709 
809 
909 
*008 
108 
207 
306 

518 
619 
719 
819 
919 
*018 
118 
217 
316 

528 
629 
729 
829 
929 
*028 
128 
227 
326 

538 
639 
739 
839 
939 
*038 
137 
237 
335 

9 

1   0.9 

2   1.8 
3   2.7 

440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

5  4.5 

441 
442 
443 
444 
445 
446 
447 
448 
449 

444 

542 
640 
738 
836 
933 
65  031 
'  128 
225 

454 
552 
650 
748 
846 
943 
040 
137 
234 

464 
562 
660 
758 
856 
953 
050 
147 
244 

473 
572 
670 
768 
865 
963 
060 
157 
254 

483 
582 
680 
777 
875 
972, 
070 
167 
263 

493 
591 
689 
787 
885 
982 
079 
176 
273 

503 
601 
699 
797 
895 
992 
089 
186 
283 

513 
611 
709 
807 
904 
*002 
099 
196 
292 

523 
621 
719 
816 
914 
*011 
108 
205 
302 

532 
631 
729 
826 
924 
*021 
118 
215 
312 

7   6.3 
8  '  7.2 
9  ,  8.1 

450 

321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOG  A  Rl  TUMI  C  TA  BLES 


341 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

450 

451 
452 
453 
454 
455 
456 
457 
458 
459 

460 

461 
462 
463 
464 
465 
466 
467 
468 
469 

470 

471 
472 
473 
474 
475 
476 
477 
478 
479 

480 

481 
482 
483 
484 
485 
486 
487 
488 
489 

490 

491 
492 
493 
494 
495 
4% 
497 
498 
499 

500 

65  321 

331 

841 

350 

447 
543 
639 
734 
830 
925 
*020 
115 
210 

360 

456 
552 
648 
744 
839 
935 
*030 
124 
219 

369 

466 
562 
658 
753 
849 
944 
*039 
134 
229 

379 

475 
571 
667 
763 
858 
954 
*049 
143 
238 

389 

485 
581 
677 
772 
868 
963 
*G58 
153 
247 

398 

495 
591 
686 
782 
877 
973 
*068 
162 
257 

351 

445 
539 
633 
727 
820 
913 
*006 
099 
191 

408 

504 
600 
696 
792 
887 
982 
*077 
172 
266 

861 

10 

1   1.0 
2   2.0 
3  3.0 
4  4.0 
•   5  5.0 
6  6.0 
7  I  T.O 
8  8.0 
9  9.0 

9 

0.9 

1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
8   7.2 
9  |  8.1 

8 

0.8 
1.6 
2.4 
3.2 
4.0 
I  4.8 
5.6 
8  6.4 
9   7.2 

418 
514 
610 
706 
801 
896 
992 
66  087 
181 

427 
523 
619 
715 
811 
906 
*001 
096 
191 

285 

437 
533 
629 
725 
820 
916 
*011 
106 
200 

276 

295 

304 

398 
492 
586 
680 
773 
867 
960 
052 
145 

314 

408 
602 
596 
689 
783 
876 
969 
062 
154 

323 

417 
511 
605 
699 
792 
885 
•978 
071 
164 

332 

427 
521 
614 

708 
801 
894 
987 
080 
173 

342 

370 
464 
558 
652 
745 
839 
932 
67025 
117 

380 
474 
567 
661 
755 
848 
941 
034 
127 

389 
483 
577 
671 
764 
857 
950 
043 
136 

436 
530 
624 
717 
811 
904 
997 
089 
182 

455 
549 
642 
736 
829 
922 
*015 
108 
201 

210 

219 

228 

237 

247 

256 

265 

274 

284 

376 
468 
560 
651 
742 
834 
925 
*015 
106 

293 

385 
477 
569 
660 
752 
843 
934 
*024 
115 

302 
394 
486 
578 
669 
761 
852 
943 
68  034 

311 
403 
495 
587 
679 
770 
861 
952 
043 

321 
413 
504 
596 
688 
779 
870 
961 
052 

330 
422 
514 
605 
697 
788 
879 
970 
061 

339 
431 
523 
614 
706 
797 
888 
979 
070 

348 
440 
532 
624 
715 
806 
897 
988 
079 

169 

357 
449 
541 
633 
724 
815 
906 
997 
088 

367 
459 
550 
642 
733 
825 
916 
*006 
097 

124 

133 

224 
314 
404 
494 
583 
673 
762 
851 
940 

142 

233 
323 
413 
502 
592 
681 
771 
860 
949 

151 

242 
332 
422 
511 
601 
690 
780 
869 
958 

160 

178 

187 

278 
368 
458 
547 
637 
726 
815 
904 
993 

196 

287 
377 
467 
556 
646 
735 
824 
913 
*002 

205 

215 
305 
395 
485 
574 
664 
753 
842 
931 

251 
341 
431 
520 
610 
699 
789 
878 
966 

260 
350 
440 
529 
619 
708 
797 
886 
975 

269 
359 
449 
538 
628 
717 
806 
895 
984 

296 
386 
476 
565 
655 
744 
833 
922 
*011 

69020 

028 

037 

046 

055 

064 

073 

082 

090 

099 

108 
197 
285 
373 
461 
548 
636 
723 
810 

117 
205 
294 
381 
469 
557 
644 
732 
819 

126 
214 
302 
390 
478 
566 
653 
740 
827 

135 
223 
311 
399 

487 
574 
662 
749 
836 

144 
232 
320 
408 
496 
583 
671 
758 
845 

152 
241 
329 
417 
504 
592 
679 
767 
854 

161 
249 
338 
425 
513 
601 
688 
775 
862 

170 
258 
346 

434 

522 
609 
697 
784 
871 

179 
267 
355 
443 
531 
618 
705 
793 
880 

188 
276 
364 
452 
539 
627 
714 
801 
888 

975 

897 

906 

914 

923 

932 

940 

949 

958 

966 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

342 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

500 

501 

502 
503 
504 
505 
506 
507 
508 
509 

510 

511 
512 
513 
514 
515 
516 
517 
518 
519 

520 

521 

522 
523 
524 
525 
526 
527 
528 
529 

530 

531 
532 
533 
534 
535 
536 
537 
538 
539 

540 

541 
542 
543 
544 
545 
546 
547 
548 
549 

550 

69  897 

906 

992 
079 
165 
252 
338 
424 
509 
595 
680 

914 

923 

*010 
096 
183 
269 
355 
441 
526 
612 
697 

783 

932 

940 

949 

*036 
122 
209 
295 
381 
467 
552 
638 
723 

958 

*044 
131 
217 
303 
389 
475 
561 
646 
731 

966 

*053 
140 
226 
312 
398 
484 
569 
655 
740 

975 

*062 
148 
234 
321 
406 
492 
578 
663 
749 

9 

0.9 
1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 

8 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.3 

7 

1  I  0.7 
2  1.4 
8  2.1 
4  2.8 
5  3.5 
6  4.2 
7  4.9 
8  56 
9  6.3 

984 
70  070 
157 
243 
329 
415 
501 
586 
672 

*001 
088 
174 
260 
346 
432 
518 
603 
689 

774 

*018 
105 
191 
278 
364 
449 
535 
621 
706 

791 

*027 
114 
200 
286 
372 
458 
544 
629 
714 

757 

766 

800 

808 

817 

825 

834 

842 
927 
71  012 
096 
181 
265 
349 
433 
517 

600 

851 
935 
020 
105 
189 
273 
357 
441 
525 

609 

859 
944 
029 
113 
198 
282 
366 
450 
533 

617 

868 
952 
037 
122 
206 
290 
374 
458 
542 

625 

876 
961 
046 
130 
214 
299 
383 
466 
550 

634 

885 
969 
054 
139 
223 
307 
391 
475 
559 

642 

893 
978 
063 
147 
231 
315 
399 
483 
567 

650 

902 
986 
071 
155 
240 
324 
408 
492 
575 

910 
995 
079 
164 
248 
332 
416 
500 
584 

667 

919 
*003 
088 
172 
257 
341 
425 
508 
592 

659 

675 

759 
842 
925 
*008 
090 
173 
255 
337 
419 

501 

684 
767 
850 
933 
72  016 
099 
181 
263 
346 

692 
775 
858 
941 
024 
107 
189 
272 
354 

700 
784 
867 
950 
032 
115 
198 
280 
362 

709 
792 
875 
958 
041 
123 
206 
288 
370 

717 
800 
883 
966 
049 
132 
214 
296 
378 

725 
809 
892 
975 
057 
'140 
222 
304 
387 

734 
817 
900 
983 
066 
148 
230 
313 
395 

742 
825 
908 
991 
074 
156 
239 
321 
403 

750 
834 
917 
999 
082 
165 
247 
329 
411 

493 

428 

436 

444 

452 

460 

469 

477 

485 

509 
591 
673 
754 
835 
916 
997 
73  078 
159 

518 
599 
681 
762 
843 
925 
*006 
086 
167 

247 

526 
607 
689 
770 
852 
933 
*014 
094 
175 

255 

534 
616 
697 
779 
860 
941 
*022 
102 
183 

542 
624 
705 
787 
868 
949 
*030 
111 
191 

550 
632 
713 
795 
876 
957 
*038 
119 
199 

558 
640 
722 
803 
884 
965 
*046 
127 
207 

567 
648 
730 
811 
892 
973 
*054 
135 
215 

296 

575 
656 
738 
819 
900 
981 
*062 
143 
223 

304 

583 
665 
746 
827 
908 
989 
*070 
151 
231 

312 

392 
472 
552 
632 
711 
791 
870 
949 
*028 

239 

263 

272 

280 

360 
440 
520 
600 
679 
759 
838 
918 
997 

288 

320 
400 
480 
560 
640 
719 
799 
878 
957 

328 
408 
488 
568 
648 
727 
807 
886 
965 

336 
416 
496 
576 
«56 
735 
815 
894 
973 

344 
424 
504 
584 
664 
743 
823 
902 
981 

352 
432 
512 
592 
672 
751 
830 
910 
989 

368 
448 
528 
608 
687 
767 
846 
926 
*005 

376 
456 
536 
616 
695 
775 
854 
933 
*013 

092 

384 
464 
544 
624 
703 
783 
862 
941 
*020 

74036 

044 

052 

060 

068 

076 

084 

099 

107 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


343 


N. 

L.O 

1 

2 

3 

4 

5 

G 

7 

8 

9 

P.P. 

550 

74  036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

651 
552 
553 
554 
555 
556 
557 
558 
559 

115 
194 
273 
351 
429 
507 
586 
663 
741 

123 

202 
280 
359 
437 
515 
593 
671 
749 

131 
210 

288 
367 
445 
523 
601 
679 
7'57 

139 

218 
296 
374 
453 
531 
609 
687 
764 

147 
225 
304 
382 
461 
539 
617 
695 
772 

155 
233 
312 
390 

468 
547 
624 
702 
780 

162 
241 
320 
398 
476 
554 
632 
710 
788 

170 
249 
327 
406 

484 
562 
640 
718 
796 

178 
257 
335 
414 
492 
570 
648 
726 
803 

186 
265 
343 
421 
500 
578 
656 
733 
811 

560 

819 

827 

834 

842 

850 

858 

865 

873 

881 

889 

g 

561 
562 
563 
564 
565 
566 
567 
568 
569 

896 
974 
75  051 
128 
205 
282 
358 
435 
511 

904 
981 
059 
136 
213 
289 
366 
442 
519 

912 
989 
066 
143 
220 
297 
374 
450 
526 

920 
997 
074 
151 
228 
305 
381 
458 
534 

927 
*005 
082 
159 
236 
312 
389 
465 
542 

935 
*012 
089 
166 
243 
320 
397 
473 
549 

943 

*020 
097 
174 
251 
328 
404 
481 
557 

950 
*028 
105 
182 
259 
335 
412 
488 
565 

958 
*035 
113 
189 
266 
343 
420 
496 
572 

966 
*043 
120 
197 
274 
351 
427 
504 
580 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
8   6.4 
9   7.2 

570 

587 

595 

603 

610 

618 

626 

633 

641 

648 

656 

571 
572 
573 
574 
575 
576 
577 
578 
579 

664 
740 
815 
891 
967 
76  042 
118 
193 
268 

671 
747 
823 
899 
974 
050 
125 
200 
275 

679 
755 
831 
906 
982 
057 
133 
208 
283 

686 
762 
838 
914 
989 
065 
140 
215 
290 

694 
770 
846 
921 
997 
072 
148 
223 
298 

702 
778 
853 
929 
*005 
080 
155 
230 
305 

709 
785 
861 
937 
*012 
087 
163 
238 
313 

717 
793 
868 
944 
*020 
095 
170 
245 
320 

724 

800 
876 
952 
*027 
103 
178 
253 
328 

732 
808 
884 
959 
*035 
110 
185 
260 
335 

580 

343 

350 

358 

365 

373 

380 

388 

395 

403 

410 

7 

581 
582 
583 
584 
585 
586 
587 
588 
589 

418 
492 
567 
641 
716 
790 
864 
938 
77  012 

425 
500 
574 
649 
723 
797 
871 
945 
019 

433 
507 
582 
656 
730 
805 
879 
953 
026 

440 
515 
589 
664 
738 
812 
886 
960 
034 

448 
522 
597 
671 
745 
819 
893 
967 
041 

455 
530 
604 
678 
753 
827 
901 
975 
048 

462 
537 
612 
686 
760 
834 
908 
982 
056 

470 
545 
619 
693 
768 
842 
916 
989 
063 

477 
552 
626 
701 
775 
849 
923 
997 
070 

485 
559 
634 
708 
782 
856 
930 
*004 
078 

1  0.7 
2  1.4 
3   2.1 
4   2.8 
5  3.5 
6  4.2 
7   4.9 
8   5.6 
9  6.S 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144 

151 

591 
592 
593 
594 
595 
596 
597 
598 
599 

159 
232 
305 
379 
452 
525 
597 
670 
743 

166 
240 
313 
386 
459 
532 
605 
677 
750 

173 
247 
320 
393 
466 
539 
612 
685 
757 

181 
254 
327 
401 
474 
546 
619 
692 
764 

188 
262 
335 
408 
481 
554 
627 
699 
772 

195 
269 
342 
415 
488 
561 
634 
706 
779 

203 
276 
349 
422 
495 
568 
641 
714 
786 

210 
283 
357 
430 
503 
576 
648 
721 
793 

217 
291 
364 
437 
510 
583 
656 
728 
801 

225 
298 
371 
444 
517 
590 
663 
735 
808 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

344 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

600 

77  815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

601 

602 
603 
604 
605 
606 
607 
608 
609 

887 
960 
78  032 
104 
176 
247 
319 
390 
462 

895 
967 
039 
111 
183 
254 
326 
398 
469 

902 
974 
046 
118 
190 
262 
333 
405 
476 

909 
981 
053 
125 
197 
269 
340 
412 
483 

916 
988 
061 
132 
204 
276 
347 
419 
490 

924 
996 
068 
140 
211 
283 
355 
426 
497 

931 
*003 
075 
147 
219 
290 
362 
433 
504 

938 
*010 
082 
154 
226 
297 
369 
440 
512 

945 

*017 
089 
161 
233 
305 
376 
447 
519 

952 
*025 
097 
168 
240 
312 
383 
455 
526 

8 

1   0.8 
2   1.6 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

4   8.2 

611 
612 
613 
614 
615 
616 
617 
618 
619 

604 
675 
746 

817 
888 
958 
79  029 
099 
169 

611 
682 
753 
824 
895 
965 
036 
106 
176 

618 
689 
760 
831 
902 
972 
043 
113 
183 

625 
696 
767 
838 
909 
979 
050 
120 
190 

633 
704 
774 
845 
916 
986 
057 
127 
197 

640 
711 

781 
852 
923 
993 
064 
134 
204 

647 
718 
789 
859 
930 
*000 
071 
141 
211 

654 
725 
796 
866 
937 
*007 
078 
148 
218 

661 
732 
803 
873 
944 
*014 
085 
155 
225 

668 
739 
810 
880 
951 
*021 
092 
162 
232 

6   4.8 
7   5.6 
8   6.4 

9  j  7.2 

620 

239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

621 
622 
623 
624 
625 
626 
627 
628 
629 

309 
379 
449 
518 
588 
657 
727 
796 
865 

316 
386 
456 
525 
595 
664 
734 
803 
872 

323 
393 
463 
532 
602 
671 
741 
810 
879 

330 
400 
470 
539 
609 
678 
748 
817 
886 

337 
407 
477 
546 
616 
685 
754 
824 
893 

344 
414 
484 
553 
623 
692 
761 
831 
900 

351 
421 
491 
560 
630 
699 
768 
837 
906 

358 
428 
498 
567 
637 
706 
775 
844 
913 

365 
435 
505 
574 
644 
713 
782 
851 
920 

372 
442 
511 
581 
650 
720 
789 
858 
927 

1   0.7 
2  1  1.4 
3  2.1 
4   2.S 
5  3.5 
6   4.2 
7   4.9 
8   5.6 
9  6.3 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

9% 

631 
632 
633 
634 
635 
636 
637 
638 
639 

80003 
072 
140 
209 
277 
346 
414 
482 
550 

010 
079 
147 
216 
284 
353 
421 
489 
557 

017 
085 
154 
223 
291 
359 
428 
496 
564 

024 
092 
161 
229 
298 
366 
434 
502 
570 

030 
099 
168 
236 
305 
373 
441 
509 
577 

037 
106 
175 
243 
312 
380 
448 
516 
584 

044 
113 
182 
250 
318 
387 
455 
523 
591 

051 
120 
188 
257 
325 
393 
462 
530 
598 

058 
127 
195 
264 
332 
400 
468 
536 
604 

065 
134 
202 
271 
339 
407 
475 
543 
611 

6 

1  0.6 
1.1 

1.8 

640 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

,  3.0 

641 
642 
643 
644 
645 
646 
647 
648 
649 

686 
754 
821 
889 
956 
81  023 
090 
158 
224 

693 
760 
828 
895 
963 
030 
097 
164 
231 

699 
767 
835 
902 
969 
037 
104 
171 
238 

706 
774 
841 
909 
976 
043 
111 
178 
245 

713 
781 
848 
916 
983 
050 
117 
184 
251 

720 
787 
855 
922 
990 
057 
124 
191 
258 

726 
794 
862 
929 
996 
064 
131 
198 
265 

733 
801 
868 
936 
*003 
070 
137 
204 
271 

740 
808 
875 
943 
*010 
077 
144 
211 
278 

747 
814 
882 
949 
*017 
084 
151 
218 
285 

7  j  4.2 
8  4.8 
9  5.4 

650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


345 


N. 

L.O 

1 

298 

2 

305 

3 

311 

4 

5 

6 

331 

7 

338 

8 

345 

9 

351 

P.P. 

650 

651 
652 
653 
654 
655 
656 
657 
658 
659 

660 

6fil 
662 
663 
664 
665 
666 
667 
668 
669 

670 

671 
672 
673 
674 
675 
676 
677 
678 
679 

680 

681 
682 
683 
684 
685 
686 
687 
688 
689 

690 

691 

692 
693 
694 
695 
696 
697 
698 
699 

700 

81  291 

318 

325 

7 

1  O.T 
2   1.4 
3  2.1 

4   2.8 
5  3.5 
6  4.2 
7   4.9 
8  5.6 
9  6.3 

6 

1   0.6 
2   1.2 
1.8 
'  2.4 
3.0 
3.6 
4.2 
4.8 
5.4 

358 
425 
491 
558 
624 
690 
757 
823 
889 

365 
431 
498 
564 
631 
697 
763 
829 
895 

371 
438 
505 
571 
637 
704 
770 
836 
902 

378 
445 
511 
578 
644 
710 
776 
842 
908 

385 
451 
518 
584 
651 
717 
783 
849 
915 

391 
458 
525 
591 
657 
723 
790 
856 
921 

398 
465 
531 
598 
664 
730 
796 
862 
928 

405 
471 
538 
604 
671 
737 
803 
869 
935 

411 

478 
544 
611 
677 
743 
809 
875 
941 

418 
485 
551 
617 
684 
750 
816 
882 
948 

954 

961 

968 

_974 

040 
105 
171 
236 
302 
367 
432 
497 
562 

981 

046 
112 
178 
243 
308 
373 
439 
504 
569 

633 

987 

994 

*000 

*007 

*014 

079 
145 
210 
276 
341 
406 
471 
636 
601 

82  020 
086 
151 
217 
282 
347 
413 
478 
543 

027 
092 
158 
223 
289 
354 
419 
484 
549 

033 

099 
164 
230 
295 
360 
426 
491 
556 

053 
119 
184 
249 
315 
380 
445 
510 
575 

640 

060 
125 
191 
256 
321 
387 
452 
517 
582 

066 
132 
197 
263 
328 
393 
458 
523 
588 

653 

073 
138 
204 
269 
334 
400 
465 
530 
595 

659 

607 

614 

620 

627 

646 

666 

672 
737 
802 
866 
930 
995 
83  059 
123 
187 

679 
743 
808 
872 
937 
*001 
065 
129 
193_ 

257 

685 
750 
814 
879 
943 
*008 
072 
136 
200 

692 
756 
821 
885 
950 
*014 
078 
142 
206 

698 
763 
827 
892 
956 
*020 
085 
149 
213 

705 
769 
834 
898 
963 
*027 
091 
155 
219 

711 
776 
840 
905 
969 
*033 
097 
161 
225 

718 
782 
847 
911 
975 
*040 
104 
168 
232 

724 
789 
853 
918 
982 
*046 
110 
174 
238 

730 
795 
860 
924 
988 
*052 
117 
181 
245 

251 

264 

270 

334 
398 
461 
525 
588 
651 
715 

JZ 

904 

276 

283 

289 

296 

359 
423 
487 
550 
613 
677 
740 
803 
866 

302 

366 
429 
493 
556 
620 
683 
746 
809 
872 

308 

315 
378 
442 
506 
569 
632 
696 
759 
822 

321 
385 
448 
512 
575 
639 
702 
765 
828 

891 

327 
391 
455 
518 
582 
645 
708 
771 
835 

340 

404 
467 
531 
594 
658 
721 
784 
847 

910 

347 
410 
474 
537 
601 
664 
727 
790 
853 

916 

353 
417 
480 
544 
607 
670 
734 
797 
860 

923 

372 
436 
499 
563 
626 
689 
753 
816 
879 

885 

897 

929 

992 
055 
117 
180 
242 
305 
367 
429 
491 

553 

935 

942 

948 
84  Oil 
073 
136 
198 
261 
323 
386 
448 

954 
017 
080 
142 
205 
267 
330 
392 
454 

960 
023 
086 
148 
211 
273 
336 
398 
460 

967 
029 
092 
155 
217 
280 
342 
404 
466 

528 

973 
036 
098 
161 
223 
286 
348 
410 
473 

979 
042 
105 
167 
230 
292 
354 
417 
479 

985 
048 
111 
173 
236 
298 
361 
423 
485 

547 

998 
061 
123 
186 
248 
311 
373 
435 
497 

*004 
067 
130 
192 
255 
317 
379 
442 
504 

510 

516 

522 

535 

&41 

559 

566 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

346 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

———————— 

P.P. 

700 

84  510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

701 
702 
703 
704 
.  705 
706 
707 
708 
709 

572 
634 
696 
757 
819 
880 
942 
85  003 
065 

578 
640 
702 
763 
825 
887 
948 
009 
071 

584 
646 
708 
770 
831 
893 
954 
016 
077 

590 

652 
714 
776 
837 
899 
960 
022 
083 

597 
658 
720 
782 
844 
905 
967 
028 
089 

603 
665 
726 
788 
850 
911 
973 
034 
095 

609 
671 
733 
794 
856 
917 
979 
040 
101 

615 
677 
739 
800 
862 
924 
985 
046 
107 

621 
683 
745 
807 
868 
930 
991 
052 
114 

628 
689 
751 
813 
874 
936 
997 
058 
120 

7 

1  0.7 
2   1.4 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

3   2.1 

4   2.8 

711 

712 
713 
714 
715 
716 
717 
718 
719 

187 
248 
309 
370 
431 
491 
552 
612 
673 

193 
254 
315 
376 
437 
497 
558 
618 
679 

199 
260 
321 
382 
443 
503 
564 
625 
685 

205 
266 
327 
388 
449 
509 
570 
631 
691 

211 
272 
333 
394 
455 
516 
576 
637 
697 

217 
278 
339 
400 
461 
522 
582 
643 
703 

224 

285 
345 
406- 
467 
528 
588 
649 
709 

230 
291 
352 
412 
473 
534 
594 
655 
715 

236 
297 
358 
418 
479 
540 
600 
661 
721 

242 
303 
364 
425 
485 
546 
606 
667 
727 

5  3.5 
6   4.2 
T   4.9 
8  5.6 
9  6.3 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

721 
722 
723 
724 
725 
726 
727 
728 
729 

794 
854 
914 
974 
86  034 
094 
153 
213 
273 

800 
860 
920 
980 
040 
100 
159 
219 
279 

806 
866 
926 
986 
046 
106 
165 
225 
285 

812 
872 
932 
992 
052 
112 
171 
231 
291 

818 
878 
938 
998 
058 
118 
177 
237 
297 

824 
884 
944 
*004 
064 
124 
183 
243 
303 

830 
890 
950 
*010 
070 
130 
189 
219 
308 

836 
896 
956 
*016 
076 
136 
195 
255 
314 

842 
902 
962 
*022 
082 
141 
201 
261 
320 

848 
908 
968 
*028 
088 
147 
207 
267 
326 

6 

1   n.f? 
2   1.2 
3   1.8 
4  2.4 
5  3.0 
6  3.6 
7  4.2 
8  4.8 
9  5.4 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 

732 
733 
734 
735 
736 
737 
738 
739 

392 
451 
510 
570 
629 
688 
747 
806 
864 

398 
457 
516 
576 
635 
694 
753 
812 
870 

404 
463 
522 
581 
641 
700 
759 
817 
876 

410 
469 
528 
587 
646 
705 
764 
823 
882 

415 
475 
534 
593 
652 
711 
770 
829 
888 

421 
481 
540 
599 
658 
717 
776 
835 
894 

427 
487 
546 
605 
664 
723 
782 
841 
900 

433 
493 
552 
611 
670 
729 
788 
847 
906 

439 
499 
558 
617 
676 
735 
794 
853 
911 

445 

504 
564 
623 
682 
741 
800 
859 
917 

5 

0.5 
1.0 
1.5 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

2.5 

741 

742 
743 
744 
745 
746 
747 
748 
749 

982 
87  040 
099 
157 
216 
274 
332 
390 
448 

988 
046 
105 
163 
221 
280 
338 
396 
454 

994 
052 
111 
169 
227 
286 
344 
402 
460 

999 
058 
116 
175 
233 
291 
349 
408 
466 

*005 
064 
122 
181 
239 
297 
355 
413 
471 

*011 
070 
128 
186 
245 
303 
361 
419 
477 

*017 
075 
134 
192 
251 
309 
367 
425 
483 

*023 
081 
140 
198 
256 
315 
373 
431 
489 

*029 
087 
146 
204 
262 
320 
379 
437 
495 

*035 
093 
151 
210 
268 
326 
384 
442 
.500 

8.5 
4.0 
46 

750 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

N. 

L.O 

1 

•2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


347 


N. 

750 

751 
752 
753 
754 
755 
756 
757 
758 
759 

760 

761 

762 
763 
764 
765 
766 
767 
768 
769 

770 

771 
772 
773 
774 
775 
776 
777 
778 
779 

780 

781 
782 
783 
784 
785 
786 
787 
788 
789 

790 

791 
792 
793 
794 
795 
796 
797 
798 
799 

800 

L.O 

87  506 

1 

512 

570 
628 
685 
743 
800 
858 
915 
973 
030 

2 

518 

576 
633 
691 
749 
806 
864 
921 
978 
036 

3 

523 

581 
639 
697 
754 
812 
869 
927 
984 
041 

4 

529 

587 
645 
703 
760 
818 
875 
933 
990 
047 

5 

535 

6 

7 

8 

9 

P.P. 

541 

547 

552 

558 

6 

1  0.6 
2   1.2 
3  1.8 
4  2.4 
5  3.0 
6  3.6 
7   4.2 
8  4.8 
9  5.4 

5 

1  0.5 
2  1.0 
3  1.5 
4  2.0 
5   2.5 
6  3.0 
7  3.5 
8  4.0 
9  4.5 

564 
622 
679 
737 
795 
852 
910 
967 
88  024 

593 
651 
708 
766 
823 
881 
938 
996 
053 

599 
656 
714 
772 
829 
887 
944 
*001 
058 

604 
662 
720 
777 
835 
892 
950 
*007 
064 

610 
668 
726 
783 
841 
898 
955 
*013 
070 

616 
674 
731 
789 
846 
904 
961 
*018 
076 

133 

081 

087 

093 

098 

104 

110 

116 

121 

127 

138 
195 
252 
309 
366 
423 
480 
536 
593 

144 
201 
258 
315 
372 
429 
485 
542 
598 

655 

150 
207 
264 
321 
377 
434 
491 
647 
604 

156 
213 
270 
326 
383 
440 
497 
553 
610 

666 

161 
218 
275 
332 
389 
446 
502 
559 
615 

672 

167 
224 
281 
338 
395 
451 
508 
564 
621 

677 

173 

230 
2S7 
343 
400 
457 
513 
570 
627 

178 
235 
292 
349 
406 
463 
519 
576 
632 

184 
241 
298 
355 
412 
468 
525 
581 
638 

190 
247 
304 
360 
417 
474 
530 
587 
643 

700 

649 

660 

683 

689 

694 

705 
762 
818 
874 
930 
986 
89042 
098 
154 

711 
767 
824 
880 
936 
992 
048 
104 
159 

717 
773 
829 
885 
941 
997 
053 
109 
165 

722 
779 
835 
891 
947 
*003 
059 
115 
170 

728 
784 
840 
897 
953 
*009 
064. 
120 
176 

734 
790 
846 
902 
958 
*014 
070 
126 
182 

739 
795 
852 
908 
964 
*020 
076 
131 
187 

745 
801 
857 
913 
969 
*025 
081 
137 
193 

750 
807 
863 
919 
975 
*031 
087 
143 
198 

756 
812 
868 
925 
981 
*037 
092 
148 
204 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

315 
371 
426 
481 
537 
592 
647 
702 
757 

265 
321 
376 
432 
487 
542 
597 
653 
708 

271 
326 
382 
437 
492 
548 
603 
658 
713 

276 
332 
387 
443 
498 
553 
609 
664 
719 

774 

282 
337 
393 
448 
504 
559 
614 
669 
724 

779 

287 
343 
398 
454 
509 
564 
620 
675 
730 

293 
348 
404 
459 
515 
570 
625 
680 
735 

298 
354 
409 
465 
520 
575 
631 
686 
741 

796 

304 
360 
415 
470 
526 
581 
636 
691 
746 

310 

3G5 
421 
476 
531 
586 
642 
697 
752 

763 

768 

785 

790 

801 

856 
911 
966 
*020 
075 
129 
184 
238 
293 

347 

8071 

812 

867 
922 
977 
*031 
086 
140 
195 
249 
304 

818 
873 
927 
982 
90  037 
091 
146 
200 
255 

823 
878 
933 
988 
042 
097 
151 
206 
260 

829 
883 
938 
993 
048 
102 
157 
211 
266 

834 
889 
944 
998 
053 
108 
162 
217 
271 

840 
894 
949 
*004 
059 
113 
168 
222 
276 

845 
900 
955 
*009 
064 
119 
173 
227 
282 

851 
905 
960 
*015 
069 
124 
179 
233 
287 

862 
916 
971 
*026 
080 
135 
189 
244 
298 

309 

314 

320 

325 

331 

336 

342 

352 

358, 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

348 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

.  2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

800 

90309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

801 
802 
803 
804 
805 
806 
807 
808 
809 

363 
417 
472 
526 
580 
634 
687 
741 
795 

369 
423 
477 
531 
585 
639 
693 
747 
800 

374 

428 
482 
536 
590 
644 
698 
752 
806 

380 
434 
488 
542 
596 
650 
703 
757 
811 

385 
439 
493 
547 
601 
655 
709 
763 
816 

390 
445 
499 
553 
607 
660 
714 
768 
822 

396 
450 
504 
558 
612 
666 
720 
773 
827 

401 
455 
509 
563 
617 
671 
725 
779 
832 

407 
461 
515 
569 
623 
677 
730 
784 
838 

412 
466 
520 
574 
628 
682 
736 
789 
843 

810 

849 

854 

859 

865 

870 

•875 

881 

886 

891 

897 

811 
812 
813 
814 
815 
816 
817 
818 
819 

902 
956 
91  009 
.  062 
116 
169 
222 
275 
328 

907 
961 
014 
068 
121 
174 
228 
281 
334 

913 
966 
020 
073 
126 
180 
233 
286 
339 

918 
972 
025 
078 
132 
185 
238 
291 
344 

924 
977 
030 
084 
137 
190 
243 
297 
350 

929 
982 
036 
089 
142 
196 
249 
302 
355 

934 
988 
041 
094 
148 
201 
254 
307 
360 

940 
993 
046 
100 
153 
206 
259 
312 
365 

945 
998 
052 
105 
158 
212 
265 
318 
371 

950 
*004 
057 
110 
164 
217 
270 
323 
376 

1  1  0.6 
2   1.2 
3  i  1.8 

4  ;  2.4 
5  3.0 
6  3.6 
7  :  4.2 

8  !  4.8 
9  |  5.4 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

821 
822 
823 
824 
825 
826 
827 
828 
829 

434 
487 
540 
593 
645 
698 
751 
803 
855 

440 
492 
545 
598 
651 
703 
756 
808 
861 

445 
498 
551 
603 
656 
709 
761 
814 
866 

450 
503 
556 
609 
661 
714 
766 
819 
871 

455 
508 
561 
614 
666 
719 
772 
824 
876 

461 
514 
566 
'619 
672 
724 
777 
829 
882 

466 
519 
572 
624 
677 
730 
782 
834 
887 

471 
524 
577 
630 
682 
735 
787 
840 
892 

477 
529 
582 
635 
687 
740 
793 
845 
897 

482 
535 
587 
640 
693 
745 
798 
850 
903 

830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

5 

831 
832 
833 
834 
835 
836 
837 
838 
839 

960 
92  012 
065 
117 
169 
221 
273 
324 
376 

965 
018 
070 
122 
174 
226 
278 
330 
381 

971 
023 
075 
127 
179 
231 
283 
335 
387 

976 
028 
080 
132 
184 
236 
288 
340 
392 

981 
033 
085 
137 
189 
241 
293 
345 
397 

986 
038 
091 
143 
195 
247 
298 
350 
402 

991 
044 
096 
148 
200 
252 
304 
355 
407 

997 
049 
101 
153 
205 
257 
309 
361 
412 

*002 
054 
106 
158 
210 
262 
314 
366 
418 

*007 
059 
111 
163 
215 
267 
319 
371 
423 

| 
0.5 

:  i.o 

1.5 

:  2.0 

2.5 
3.0 
'  8.5 
8  4.0 
9   4.5 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

841 
842 
843 
844 
845 
846 
847 
848 
849 

480 
531 
583 
634 
686 
737 
788 
840 
891 

485 
536 
588 
639 
691 
742 
793 
845 
8% 

490 
542 
593 
645 
696 
747 
799 
850 
901 

495 
547 
598 
650 
701 
752 
804 
855 
906 

500 
552 
603 
655 
706 
758 
809 
860 
911 

505 
557 
609 
660 
711 
763 
814 
865 
916 

511 
562 
614 
665 
716 
768 
819 
870 
921 

516 
567 
619 
670 
722 
773 
824 
875 
927 

521 
572 
624 
675 
727 
778 
829 
881 
932 

526 
578 
629 
681 
732 
783 
834 
886 
937 

850 

942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


349 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

I 

'.P. 

850 

92  942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

851 
852 
853 
854 
855 
856 
857 
858 
859 

993 
93  044 
095 
146 
197 
24V 
298 
349 
399 

998 
049 
100 
151 
202 
252 
303 
354 
404 

*003 
054 
105 
156 
207 
258 
308 
359 
409 

*008 
059 
110 
161 
212 
263 
313 
364 
414 

*013 
064 
115 
166 
217 
268 
318 
369 
420 

*018 
069 
120 
171 
222 
273 
323 
374 
425 

*024 
075 
125 
176 
227 
278 
328 
379 
430 

*029 
080 
131 
181 
232 
283 
334 
384 
435 

*034 
085 
136 
186 
237 
288 
a39 
389 
440 

*039 
090 
141 
192 
242 
293 
344 
394 
445 

1 

2 

6 

O.ft 
1.2 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

4 

2.4 

861 
862 
863 
864' 
865 
866 
867 
868 
869 

500 
551 
601 
651 
702 
752 
802 
852 
902 

505 
556 
606 
656 
707 
757 
807 
857 
907 

510 

561 
611 
661 
712 
762 
812 
862 
912 

515 
566 
616 
666 
717 
767 
817 
867 
917 

520 
571 

621 
671 
722 
772 
822 
872 
922 

526 
576 
626 
676 

727 
777 
827 
877 
927 

531 
581 
631 
682 
732 
782 
832 
882 
932 

536 
586 
636 
687 
737 
787 
837 
887 
937 

541 
591 
641 
692 
742 
792 
842 
892 
942 

546 
596 
'646 
697 
747 
797 
847 
897 
947 

6 
7 
8 
9 

S.6 

4.2 
4.8 
5.4 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

871 
872 
873 
874 
875 
876 
877 
878 
879 

94  002 
052 
101 
151 
201 
250 
300 
349 
399 

007 
057 
106 
156 
206 
255 
305 
354 
404 

012 
062 
111 
161 
211 
260 
310 
359 
409 

017 
067 
116 
166 
216 
265 
315 
364 
414 

022 
072 
121 
171 
221 
270 
320 
369 
419 

027 
077 
126 
176 
226 
275 
325 
374 
424 

032 
082 
131 
181 
231 
280 
330 
379 
429 

037 
086 
136 
186 
236 
285 
335 
384 
433 

042 
091 
141 
191 
240 
290 
340 
389 
438 

047 
096 
146 
196 
245 
295 
345 
394 
443 

0.5 
1.0 
1.6 
2.0 
2.5 
3.0 
3.5 
4.0 
4.6 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

881 
882 
883 
884 
885 
886 
887 
888 
889 

498 
547 
596 
645 
694 
743 
792 
841 
890 

503 
552 
601 
650 
699 
748 
797 
846 
895 

507 
557 
606 
655 
704 
753 
802 
851 
900 

512 
562 
611 
660 
709 
758 
807 
856 
905 

517 
567 
616 
665 
714 
763 
812 
861 
910 

522 
571 
621 
670 
719 
768 
817 
866 
915 

527 
576 
626 
675 
724 
773 
822 
871 
919 

532 
581 
630 
CSO 
729 
778 
827 
876 
924 

537 
586 
635 
685 
734 
783 
832 
880 
929 

542 

591 
640 
689 
738 
787 
836 
885 
934 

1 
2 
3 

4 

0.4 
0.8 
1.2 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

4 

5 

1.6 
2.0 

891 

892 
893 
894 
895 
896 
897 
898 
899 

988 
95  036 
085 
134 
182 
231 
279 
328 
376 

993 
041 
090 
139 
187 
236 
284 
332 
381 

998 
046 
095 
143 
192 
240 
289 
337 
386 

*002 
051 
100 
148 
197 
245 
294 
342 
390 

*007 
056 
105 
153 
202 
250 
299 
347 
395 

*012 
061 
109 
158 
207 
255 
303 
352 
400 

*017 
066 
114 
163 
211 
260 
308 
357 
405 

*022 
071 
119 
168 
216 
265 
313 
361 
410 

*027 
075 
124 
173 
221 
270 
318 
366 
415 

*032 
080 
129 
177 
226 
274 
323 
371 
419 

6 
7 
8 
9 

2.4 
2.8 
3.2 
S.ft 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

350 


MINE  GASES  AND  VENTILATION 


N. 

L.O 

1 

2 

3 

4 

5 

6 

•7 

8 

9 

P.P. 

900 

901 
902 
903 
904 
905 
906 
907 
908 
909 

910 

911 
912 
913 
914 
915 
916 
917 
918 
919 

920 

921 
922 
923 
924 
925 
926 
927 
928 
929 

930 

931 

932 
933 
934 
935 
936 
937 
938 
939 

940 

941 
942 
943 
944 
945 
946 
947 
948 
949 

950 

95  424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

5 

0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
8  4.0 
»j  4.5 

4 

0.4 

0.8 
1.2 
1.6 
2.0 
2.4 
2.8 
8  3.2 
9  3.6 

472 
521 
569 
617 
665 
713 
761 
809 
856 

477 
525 
574 
622 
670 
718 
766 
813 
861 

482 
530 
578 
626 
674 
722 
770 
818 
866 

914 

487 
535 
583 
631 
679 
727 
775 
823 
871 

918 

492 
540 
588 
636 
684 
732 
780 
828 
875 

497 
545 
693 
641 
689 
737 
785 
832 
880 

501 
550 
598 
646 
694 
742 
789 
837 
885 

506 
554 
602 
650 
698 
746 
794 
842 
890 

938 

511 
559 
607 
655 
703 
751 
799 
847 
895 

516 
564 
612 
660 
708 
756 
804 
852 
899 

947 

904 

909 

957 
*004 
052 
099 
147 
194 
242 
289 
336 

384 

923 

971 
*019 
066 
114 
161 
209 
256 
303 
350 

928 

976 
*023 
071 
118 
166 
213 
261 
308 
355 

933 

942 

952 
999 
96  047 
095 
142 
190 
237 
284 
332 

961 
*009 
057 
104 
152 
199 
246 
294 
341 

388 

966 
*014 
061 
109 
156 
204 
251 
298 
346 

980 
*028 
076 
123 
171 
218 
265 
313 
360 

407 

985 
*033 
080 
128 
175 
223 
270 
317 
365 

412 

990 
*038 
085 
133 
180 
227 
275 
322 
369 

995 
*042 
090 
137 
185 
232 
280 
327 
374 

421 

379 

393 

398 

402 

417 

426 
473 
520 
567 
"  614 
661 
708 
755 
802 

431 
478 
525 
572 
619 
666 
713 
759 
806 

853 

435 
483 
530 
577 
624 
670 
717 
764 
811 

858 

440 
487 
534 
581 
628 
675 
722 
769 
816 

445 
492 
539 
586 
633 
680 
727 
774 
820 

867 

450 
497 
544 
591 
638 
685 
731 
778 
825 

454 
501 
648 
595 
642 
689 
736 
783 
830 

459 
506 
553 
600 
647 
694 
741 
788 
834 

881 

464 
511 
558 
605 
652 
699 
745 
792 
839 

468 
515 
562 
609 
656 
703 
750 
797 
844 

848 

862 

872 

876 

886 

890 

895 
942 
988 
97  035 
081 
128 
174 
220 
267 

900 
946 
993 
039 
086 
132 
179 
225 
271 

904 
951 
997 
044 
090 
137 
183 
230 
276 

909 
956 
*002 
049 
095 
142 
188 
234 
280 

914 
960 
*007 
053 
100 
146 
192 
239 
285 

918 
965 
*011 
058 
104 
151 
197 
243 
290 

923 
970 
*016 
063 
109 
155 
202 
248 
294 

928 
974 
*021 
067 
114 
160 
206 
253 
299 

932 
979 
*025 
072 
118 
165 
211 
257 
304 

937 
984 
*030 
077 
123 
169 
216 
262 
308 

313 

317 

364 
410 
456 
502 
548 
594 
640 
685 
731 

322 

327 

373 
419 
465 
511 
557 
603 
649 
695 
740 

331 

336 

382 
428 
474 
520 
566 
612 
658 
704 
749 

340 

345 

391 
437 
483 
529 
575 
621 
667 
713 
759 

350 

3% 
442 
488 
534 
580 
626 
672 
717 
763 

354 

359 
405 
451 
497 
543 
589 
635 
681 
727 

368 
414 
460 
606 
552 
598 
644 
690 
736 

377 
424 
470 
516 
562 
607 
653 
699 
745 

387 
433 
479 
525 
571 
617 
663 
708 
754 

400 
447 
493 
539 
585 
630 
676 
722 
768 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMIC  TABLES 


351 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

950 

97  772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

951 

952 
953 
954 
955 
956 
957 
958 
959 

818 
864 
909 
955 
98  000 
046 
091 
137 
182 

823 
868 
914 
959 
005 
050 
096 
141 
186 

827 
873 
918 
964 
009 
055 
100 
146 
191 

832 
877 
923 
968 
014 
059 
105 
150 
195 

836 
882 
928 
973 
019 
064 
109 
155 
200 

841 
886 
932 
978 
023 
068 
114 
159 
204 

845 
891 
937 
982 
028 
073 
118 
164 
209 

850 
896 
941 
987 
032 
078 
123 
168 
214 

855 
900 
946 
991 
037 
082 
127 
173 
218 

859 
905 
950 
996 
041 
087 
132 
177 
223 

960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

5 

961 
962 
963 
964 
965 
966 
967 
968 
969 

272 
318 
363 
408 
453 
498 
543 
588 
632 

277 
322 
367 
412 
457 
502 
547 
592 
637 

281 
327 
372 
417 
462 
507 
552 
597 
641 

286 
331 
376 
421 
466 
511 
556 
601 
646 

290 
336 
381 
426 
471 
516 
561 
605 
650 

295 
340 
385 
430 
475 
520 
565 
610 
655 

299 
345 
390 
435 
480 
525 
570 
614 
659 

304 
349 
394 
439 
484 
529 
574 
619 
664 

308 
354 
399 
444 
489 
534 
579 
623 
668 

313 
358 
403 
448 
493 
538 
583 
628 
673 

1  0.5 
2   1.0 
3   1.5 
4  2.0 
5  2.5 
6  S.O 
7  3.5 
8   4.0 
9  4.5 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

971 
972 
973 
974 
975 
976 
977 
978 
979 

722 
767 
811 
856 
900 
945 
989 
99  034 
078 

726 
771 
816 
860 
905 
949 
994 
038 
083 

731 
776 
820 
865 
909 
954 
998 
043 
087 

735 
780 
825 
869 
914 
958 
*003 
047 
092 

740 

784 
829 
874 
918 
963 
*007 
052 
096 

744 
789 
834 
878 
923 
967 
*012 
056 
100 

749 
793 
838 
883 
927 
972 
*016 
061 
105 

753 
798 
843 
887 
932 
976 
*021 
065 
109 

758 
802 
847 
892 
936 
981 
*025 
069 
114 

762 
807 
851 
896 
941 
985 
*029 
074 
118 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

A 

981 
982 
983 
984 
985 
986 
987 
988 
989 

167 
211 
255 
300 
344 
388 
432 
476 
520 

171 
216 
260 
304 
348 
392 
436 
480 
524 

176 
220 
264 
308 
352 
396 
441 
484 
528 

180 
224 
269 
313 
357 
401 
445 
489 
533 

185 
229 
273 
317 
361 
405 
449 
493 
537 

189 
233 
277 
322 
366 
410 
454 
498 
542 

193 
238 
282 
326 
370 
414 
458 
502 
546 

198 
242 
286 
330 
374 
419 
463 
506 
550 

202 
247 
291 
335 
379 
423 
467 
511 
555 

207 
251 
295 
339 
383 
427 
471 
515 
559 

1  0.4 

2   0.8 
3  1.2 
•  4   1.6 
5  2.0 
6  2.4 
7  2.8 
8  8.2 
9  3.6 

990 

564 

568 

572 

577 

581 

585 

590 

594 

599 

603 

991 
992 
993 
994 
995 
996 
997 
998 
999 

607 
651 
695 
739 
782 
826 
870 
913 
957 

612 
656 
699 
743 
787 
830 
874 
917 
961 

616 
660 
704 

747 
791 
835 
878 
922 
965 

621 
664 
708 
752 
795 
839 
883 
926 
970 

625 
669 
712 
756 
800 
843 
887 
930 
974 

629 
673 
717 
760 
804 
848 
891 
935 
978 

634 
677 

721 
765 
808 
852 
896 
939 
983 

638 
682 
726 
769 
813 
856 
900 
944 
987 

642 

686 
730 
774 
817 
861 
904 
948 
991 

647 
691 
734 
778 
822 
865 
909 
952 
996 

1000 

00000 

004 

009 

013 

017 

022 

026 

030 

035 

039 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

CIRCULAR  FUNCTIONS 
SINES  AND  COSINES 


353 


354 


MINE  GASES  AND  VENTILATION 


©  o° 


.00000 
.00029 
.00058 
.00087 
.00116 
.00145 
.00175 
.00204 
.00233 
.00262 
.00291 

.00320 
.00349 
.00378 
.00407 
.00436 
.00465 
.00495 
.00524 
.00553 
.00582 

.00611 
.00640 
.00669 
.00698 
.00727 
.00756 
.00785 
.00814 
.00844 
.00873 

.00902 
.00931 
.00960 
.00989 
.01018 
.01047 
.01076 
.01105 
.01134 
.01164 

.01193 
.01222 
.01251 
.01280 
.01309 
.01338 
.01367 
.01396 
.01425 
.01454 

.01483 
.01513 
.01542 
.01571 
.01600 
.01629 
.01658 
.01687 
.01716 
.01745 


.99997 
.99997 


.99997 
.99996 


.99995 
.99995 

!99995 
.99994 
.99994 
.99994 


.99987 


.99985 


.01745 
.01774 
.01803 
.01832 
.01862 
.01891 
.01920 
.01949 
.01978 
.02007 
.02036 

.02065 
.02094 
.02W3 
.02152 
.02181 
.02211 
.02240 
.02269 
.02298 
.02327 

.02356 
.02385 
.02414 
.02443 
.02472 
.02501 
.02530 
.02560 


.02647 
.02676 
.02705 
.02734 
.02763 
.02792 
.02821 
.02850 
.02879 


.02938 
.02967 
.02996 
.03025 


.03112 
.03141 
.03170 
.03199 

.03228 
.03257 
.03286 
.03316 
.03345 
.03374 
.03403 
.03432 
.03461 
.03490 


.03490 
.03519 
.03548 
.03577 


.03635 
.03664 
.03693 
.03723 
.03752 
.03781 


.03897 
.03926 
.03955 
.03984 
.04013 
.04042 
.04071 

.04100 
.04129 
.04159 
.04188 
.04217 
.04246 
.04275 
.04304 
.04333 
.04362 

.04391 
.04420 
.04449 
.04478 
.04507 
.04536 
.04565 
.04594 
.04623 
.04653 

.04682 
.04711 
.04740 
.04769 
.04798 
.04827 
.04856 
.04885 
.04914 
.04943 

.04972 
.05001 
.05030 
.05059 


.05117 
.05146 
.05175 
.05205 
.05234 


Cosine 


Cosine   Sine 


87° 


8° 


Sine 


.05234 
.05263 
.05292 
.05321 
.05350 
.05379 
.05408 
.05437 
.05466 
.05495 
.05524 

.05553 
.05582 
.05611 
.05640 


.05727 
.05756 
.05785 
.05814 

.05844 
.05873 
.05902 


.06018 
.06047 
.06076 
.06105 

.06134 
.06163 
.06192 
.06221 
.06250 
.06279 
.06308 
.06337 


.06395 

.06424 
.06453 
.06482 
.06511 
.06540 
.06569 
.06598 
.06627 
.06656 
.06685 

.06714 
.06743 
.06773 


.06918 
.06947 
.06976 


4° 


.07005 
.07034 
.07063 
.07092 
.07121 
.07150 
.07179 
.07208 
.07237 
.07266 

.07295 
.07324 
.07353 
.07382 
.07411 
.07440 
.07469 
.07493 
.07527 
.07556 

.07585 
.07614 
.07643 
.07672 
.07701 
.07730 
.07759 
.07788 
.07817 
.07846 

.07875 
.07904 
.07933 
.07962 
.07991 
.08020 
.08049 
.08078 
.08107 


.08165 
.08194 
.08223 
.08252 
.08281 
.08310 


.08426 

.08455 
.08484 
.08513 
.08542 
.08571 
.08600 
.08629 
.08658 
.08687 
.08716 


.99750 
.99748 
.99746 
.99744 
.99742 
.99740 
.99738 
.99736 

.99734 
.99731 
.99729 
.99727 
.99725 
.99723 
.99721 
.99719 
.99716 


.99666 
.99664 


.99659 
.99657 


.99649 
.99647 


.99642 


.99627 
.99625 


.99619 


85° 


SINES  AND  COSINES 


355 


/ 

j 

>° 

( 

>° 

0 

{ 

IP 

9 

0 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

.08716 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

60 

.08745 

.99617 

.10482 

.99449 

.12216 

.99251 

.13946 

.99023 

.15672 

.98764 

59 

.08774 

.99614 

.10511 

.99446 

.12245 

.99248 

.13975 

.99019 

.15701 

.98760 

58 

.08803 

.99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.157SO 

.98755 

67 

.08831 

.99609 

.10569 

.99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

.08860 

.99607 

.10597 

.99437 

.12331 

.99237 

.14061 

.99006 

.15787 

.98746 

65 

.08889 

.99604 

.10626 

.99434 

.12360 

.99233 

.14090 

.99002 

.15816 

.98741 

54 

.08918 

.99602 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

a 

.08947 

.99599 

.10684 

.99428 

.12418 

.99226 

.14148 

.98994 

.15873 

.98732 

52 

9 

.08976 

.99596 

.10T13 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

.09005 

.99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

.99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

.99588 

.10800 

.99415 

.12533 

.99211 

.142G3 

.98978 

.15988 

.98714 

48 

13 

.09092 

.99586 

.10829 

.99412 

.12562 

.99208 

.14292 

.98973 

.16017 

.98700 

47 

14 

.09121 

.99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.989C9 

.16046 

.93704 

46 

15 

.09150 

.99580 

.10887 

.99406 

.12620 

.  .09200 

.14349 

.98965 

.16074 

.98700 

45 

16 

.09179 

.99578 

.10916 

.99402 

.12649 

.99197 

.14378 

.98961 

J6103 

.98695 

41 

17 

.09208 

.99575 

.10945 

.99399 

.12678 

.99193 

.14407 

.98957 

.16132 

.98690 

43 

18 

.09237 

.99572 

.10973 

.99396 

.12706 

.99189 

.14436 

.98953 

.16160 

.08686 

42 

19 

.09266 

.99570 

.11002 

.99393 

.12735 

.99186 

.14464 

.98948 

.16189 

.98681 

41 

20 

.09295 

.99567 

.11031 

.99390 

.12764 

99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

.09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

.09353 

.99562 

.11089 

.99383 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667 

38 

23 

.09382 

.99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

24 

.09411 

.99556 

.11147 

.99377 

.12880 

.99167 

.14608 

.98927 

.16333 

.98657 

30 

25 

.09440 

.99553 

.11176 

.99374 

.12908 

.99163 

.14637 

.98923 

.16361 

.98652 

35 

26 

.09469 

.99551 

.11205 

.99370 

.12937 

.99100 

.14666 

.98919 

.16390 

.98648 

34 

27 

.09498 

.99548 

.11234 

.99367 

.12966 

.99156 

.14695 

.98914 

.16419 

.98643 

33 

28 

.09527 

.99545 

.11263 

.99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

.09556 

.99542 

.11291 

.99360 

.13024 

.99148 

.14752 

.98906 

.16476 

.98633 

31 

30 

.09585 

.99540 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

.09614 

.99537 

.11849 

.99354 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619 

S3 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.99133 

.14867 

.98889 

.16591 

.98614 

27 

34 

.09700 

.99528 

.11436 

.99344 

.13168 

.99129 

.14896 

.98884 

.16620 

.98609 

26 

85 

.09729 

.99526 

.11465 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604 

25 

36 

.09758 

.99523 

.11494 

.99337 

.13226 

.99122 

.14954 

.98876 

.16677 

.98600 

24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.16706 

.98595 

23 

38 

.09816 

.99517 

.11552 

.99331 

.13283 

.99114 

.15011 

.98867 

.16734 

.98590 

22 

39 

.09845 

.99514 

.11580 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585 

21 

40 

.09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15069 

.98858 

.16792 

.98580 

20 

41 

.09903 

.99508 

.11638 

.99320 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.99506 

.11667 

.99317 

.18399 

.99098 

.15126 

.98849 

.16849 

.98570 

13 

43 

.09961 

.99503 

.11696 

.99314 

.13427 

.99094 

.15155 

.98845 

.16878 

.98565 

17 

44 

.09990 

.99500 

.11725 

.99310 

.13456 

.99091 

.15184 

.98841 

.16906 

.98561 

16 

15 

.10019 

.99497 

.11754 

.99307 

.13485 

.99087 

.15212 

.98836 

.16935 

.98556 

15 

46 

.10048 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

.16964 

.98551 

14 

47 

.10077 

.99491 

.11812 

.99300 

.13543 

.99079 

.15270 

.98827 

.16992 

.98546 

13 

48 

.10106 

.99488 

.11840 

.99297 

.13572 

.99075 

.15299 

.98823 

.17021 

.98541 

12 

49 

.10135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

.17050 

.98536 

11 

50 

.10164 

.99482 

.11898 

.99290 

.13629 

.99067 

.15356 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15885 

.98809 

.17107 

.98526 

62 

.10221 

.99476 

.11956 

.99283 

.13687 

.99059 

.15414 

.98805 

.17136 

.98521 

69 

.10250 

.99473 

.11985 

.99279 

.13716 

.99055 

.15442 

.98800 

.17164 

.98516 

ft* 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

55 

.10308 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

99043 

.15529 

.98787 

.17250 

.98501 

57 

.10366 

.99461 

.12100 

.99265 

.13831 

99039 

.15557 

.98782 

.17279 

.984% 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

99035 

.15586 

.98778 

.17308 

98491 

59 

.10424 

.99455 

.12158 

.99258 

.13889 

99031 

.15615 

.98773 

.17336 

98486 

60 

.10453 

.99452 

.12187 

.99255 

.13917 

99027 

.15643 

.98769 

.17365 

98481 

Cosine 

Sine 

Cosine 

Bine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

f 

8-1 

o 

82 

° 

82 

o 

81 

O 

80 

» 

350 


MIN'E  GASES  AND  VENTILATION 


'  1 

] 

0° 

1 

1° 

] 

2° 

1 

3° 

] 

4° 

Sine 

Cosine 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosine 

0 

.17365 

.98481 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

60 

.17393 

.98476 

.19109 

.98157 

.20820 

.97809 

.22523 

.97430 

.24220 

.97023 

59 

.17422 

.98471 

.19138 

.98152 

.20848 

.97803 

.22552 

.97424 

.24249 

.97015 

58 

.17451 

.98466 

.19167 

.98146 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008 

57 

.17479 

.98461 

.19195 

.98140 

.20905 

.97791 

.22608 

.97411 

.24305 

.97001 

56 

.17508 

.98455 

.19224 

.98135 

.20933 

.97784 

.22637 

.97404 

.24333 

.96994 

55 

.17537 

.98450 

.19252 

.98129 

.20962 

.97778 

.22665 

.97398 

.24362 

.96987 

54 

.17565 

.98445 

.19281 

.98124 

.20990 

.97772 

.22693 

.97391 

.24390 

.96980 

53 

8 

.17594 

.98440 

.19309 

.98118 

.21019 

.97766 

.22722 

.97384 

.24418 

.96973 

52 

9 

.17623 

.98435 

.19338 

.98112 

.21047 

.97760 

.22750 

.97378 

.24446 

.96966 

51 

10 

.17651 

.98430 

'.19366 

.98107 

.21076 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

.17680 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807 

.97365 

.24503 

.96952 

49 

12 

.17708 

.98420 

.19423 

.98096 

.21132 

.97742 

.22835 

.97358 

.24531 

.96945 

48 

13 

.17737 

.98414 

.19452 

.98090 

.21161 

.97735 

.22863 

.97351 

.24559 

.96937 

47 

.H 

.17766 

.98409 

.19481 

.98084 

.21189 

.97729 

.22892 

.97345 

.24587 

.96930 

46 

15 

.17794 

.98404 

.19509 

.98079 

.21218 

.97723 

.22920 

.97338 

.24615 

.96923 

45 

16 

.17823 

.98399 

.19538 

.98073 

.21246 

.97717 

.22948 

.97331 

.24644 

.96916 

44 

17 

.17852 

.98394 

.19566 

.98067 

.21275 

.977U 

.22977 

.97325 

.24672 

.96909 

43 

18 

.17880 

.98389 

.19595 

.98061 

.21303 

.97  WS 

.23005 

.97318 

.24700 

.96902 

42 

19 

.17909 

.98383 

.19623 

.98056 

.21331 

.97698 

.23033 

.97311 

.24728 

.96894 

41 

20 

.17937 

.98378 

.19652 

.98050 

.21360 

.97692 

.23062 

.97304 

.24756 

.96887 

40 

21 

.17966 

.98373 

.19680 

.98044 

.21388 

.97686 

.23090 

.97298 

.24-784 

.96880 

39 

22 

.17995 

.98368 

.19709 

.98039 

.21417 

.97680 

.23118 

.97291 

.24813 

.96873 

38 

23 

.18023 

.98362 

.19737 

.98033 

.21445 

.97673 

.23146 

.97284 

.24841 

37 

24 

.18052 

.98357 

.19766 

.98027 

.21474 

.97667 

.23175 

.97278 

.24869 

!96858 

36 

25 

.18081 

.98352 

.19794 

.98021 

.21502 

.97661 

.23203 

.97271 

.24897 

.96851 

35 

26 

.18109 

.98347 

.19823 

.98016 

.21530 

.97655 

.23231 

.97264 

.24925 

.96844 

34 

27 

.18138 

.98341 

.19851 

.98010 

.21559 

.97648 

.23260 

.97257 

.24954 

.96837 

33 

28 

.18166 

.98336 

.19880 

.98004 

.21587' 

.97642 

.23288 

.97251 

.24982 

.96829 

82 

29 

.18195 

.98331 

.19908 

.97998 

.21616 

.97636 

.23316 

.97244 

.25010 

.96822 

31 

30 

.18224 

.98325 

.19937 

.97992 

.21644 

.97630 

.23345 

.97237 

.25038 

.96815 

30 

31 

.18252 

.98320 

.19965 

.97987 

.21672 

.97623 

.23373 

.97230 

.25066 

.96807 

29 

32 

.18281 

.98315 

.19994 

.97981 

.21701 

.97617 

.23401 

.97223 

.25094 

.96800 

28 

33 

.18309 

.98310 

.20022 

.97975 

.21729 

.97611 

.23429 

.97217 

.25122 

.96793 

27 

34 

.18338 

.98304 

.20051 

.97969 

.21758 

.97604 

.23458 

.97210 

.25151 

.96786 

26 

35 

.18367 

.98299 

.20079 

.97963 

.21786 

.97598 

.23486 

.97203 

.25179 

.96778 

25 

36 

.18395 

.98294 

.20108 

.97958 

.21814 

.97592 

.23514 

.97196 

.25207 

.96771 

24 

37 

.18424 

.98288 

.20136 

.97952 

.21843 

.97585 

.23542 

.97189 

.25235 

.96764 

23 

38 

.18452 

.98283 

.20165 

.97946 

.21871 

.97579 

.23571 

.97182 

.25263 

.96756 

22 

39 

.18481 

.98277 

.20193 

.97940 

.21899 

.97573 

.23599 

.97176 

.25291 

.96749 

21 

40 

.18509 

.98272 

.20222 

.97934 

.21928 

.97566 

.23627 

.97169 

.25320 

.96742 

20 

41 

.18538 

.98267 

.20250 

.97928 

.21956 

.97560 

.23656 

.97162 

.20348 

.96784 

19 

42 

.18567 

.98261 

.20279 

.97922 

.21985 

.97553 

.23684 

.97155 

.25376 

.96727 

18 

43 

.18595 

.98256 

.20307 

.97916 

.22013 

.97547 

.23712 

.97148 

.25404 

.96719 

17 

44 

.18624 

.98250 

.20336 

.97910 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

16 

45 

.18652 

98245 

.20364 

.97905 

.22070 

.97534 

.23769 

.97134 

.25460 

.96705 

15 

46 

.18681 

.98240 

.20393 

.97899 

.22098 

.97528 

.23797 

.97127 

.25488 

.96697 

14 

47 

.18710 

.98234 

.20421 

.97893 

.22126 

.97521 

.23825 

.97120 

.25516 

.96690 

13 

48 

.18738 

.98229 

.20450 

.97887 

.22155 

.97515 

.23853 

.97113 

.25545 

96682 

12 

49 

.18767 

.98223 

.20478 

.97881 

.22183 

.97508 

.23882 

.97106 

.25573 

96675 

11 

60 

.18795 

.98218 

.20507 

.97875 

.22212 

.97502 

.23910' 

.97100 

.25601 

96667 

10 

51 

.18824 

.98212 

.20535 

.97869 

.22240 

.97496 

.23938 

.97093 

.25629 

96660 

9 

62 

.18852 

.98207 

.20563 

.97863 

.22268 

.97489 

.23966 

.97086 

.25657 

96653 

8 

63 

.18881 

.98201 

.20592 

.97857 

.22297 

.97483 

.23995 

.97079 

.25685 

96645 

7 

64 

.18910 

.98196 

.20620 

.97851 

.22325 

.97476 

.24023 

.97072 

.25713 

96638 

6 

55 

.18938 

.98190 

.20649 

.97845 

.22353 

.97470 

.24051 

.97065 

.25741 

96630 

6 

66 

.18967 

.98185 

.20677 

.97839 

.22382 

.97463 

.24079 

.97058 

.25769 

96623 

4 

67 

.18995 

.98179 

.20706 

.97833 

.22410 

.97457 

.24108 

.97051 

.25798 

96615 

3 

68 

.19024 

.98174 

.20734 

.97827 

.22438 

.97450 

.24136 

.97044 

.25826 

96608 

2 

69 

.19052 

.98168 

.20763 

.97821 

.22467 

.97444 

.24164 

.97037 

.25854 

96600 

1 

00 

.19081 

.98163 

.20791 

.97815 

22495 

.97437 

.24192 

.97030 

25882 

96593 

0 

OMift* 

fiiac 

Coaina 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Coein* 

Sine 

79 

» 

7S 

9  ' 

77 

5 

76< 

> 

75C 

• 

SINES  AND  COSINES 


357 


/ 

1 

5° 

1 

5° 

1 

7° 

1 

}° 

1< 

)° 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.25882 

.96593 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

60 

.25910 

.96585 

.27592 

.96118 

.29265 

.95622 

.30929 

.95097 

.32584 

.94542 

69 

.25938 

.96578 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94533 

68 

.25966 

.96570 

.27648 

.96102 

.29321 

.95605 

.30985 

.95079 

.32639 

.94523 

57 

.25994 

.96562 

.27676 

.96094 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

56 

.26022 

.96555 

.27704 

.96086 

.29376 

.95588 

.31040 

.95061 

.32694 

.94604 

55 

.26050 

.96547 

.27731 

.96078 

.29404 

.95579 

.31068 

.95052 

.32722 

.94495 

64 

.26079 

.96540 

.27759 

.96070 

.29432 

.95571 

.81095 

.95043 

.32749 

.94485 

53 

.26107 

.96532 

.27787 

.96062 

.29460 

.95562 

.31123 

.95033 

.32777 

.94476 

52 

.26135 

.96524 

.27815 

.96054 

.29487 

.95554 

.31151 

.95024 

.32804 

.94466 

51 

10 

.26163 

.96517 

.27843 

.96046 

.29515 

.95545 

.31178 

.95015 

.32832 

.94467 

50 

11 

.26191 

.96509 

.27871 

.96037 

.29543 

.95536 

.31206 

.95006 

.32859 

.94447 

49 

12 

.26219 

.96502 

.27899 

.96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

.26247 

.96494 

.27927 

.96021 

.29599 

.95519 

.31261 

.94988 

.32914 

.94428 

47 

14 

.26275 

.96486 

.27955 

.96013 

.29626 

.95511 

.31289 

.94979 

.32942 

.94418 

46 

15 

.26303 

.96479 

.27983 

.96005 

.29654 

.95502 

.81316 

.94970 

.32969 

.94409 

45 

16 

.26331 

.96471 

.28011 

.95997 

.29682 

.95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

.26359 

.96463 

.28039 

.95989 

.29710 

.95485 

.31372 

.94952 

.83024 

.94390 

43 

18 

.26387 

.96456 

.28067 

.95981 

.29737 

.95476 

.31399 

.94943 

.33051 

.94380 

42 

19 

.26415 

.96448 

.28095 

.95972 

.29765 

.95467 

.31427 

.94933 

.33079 

.94370 

41 

20 

.26443 

.96440 

.28123 

.95964 

.29793 

.95459 

.31454 

.94924 

.83106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.29821 

.95450 

.31482 

.94915 

.33134 

.94351 

39 

22 

.26500 

.96425 

.28178 

.95948 

.29849 

.95441 

.81510 

.94906 

.33161 

.94342 

88 

23 

.26528 

.96417 

.28206 

.95940 

.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

25 

.26584 

.96402 

.28262 

.95923 

.29932 

.95415 

.31593 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28290 

.95915 

.29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.26640 

.96386 

.28318 

.95907 

.29987 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

.33326 

.94284 

32 

29 

.26696 

.96371 

.28374 

.95890 

.30043 

.95380 

.31703 

.94842 

.83353 

.94274 

31 

80 

.26724 

.96363 

.28402 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

.94264 

30 

31 

.26752 

.96355 

.28429 

.95874 

.30098 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.26780 

.96347 

.28457 

.95865 

.30126 

.95354 

.31786 

.94814 

.33436 

.94245 

28 

33 

.26808 

.96340 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.28513 

.95849 

.30182 

.95337 

.31841 

.94795 

.33490 

.94225 

26 

35 

.26864 

.96324 

.28541 

.95841 

.30209 

.95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28569 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

3T 

.26920 

.96308 

.28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

.95301 

.81951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.96293 

.28652 

.95807 

.30320 

.95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.28708 

.95791 

.30376 

.95275 

.82034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30403 

.95266 

.82061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

.32089 

.94712 

.83737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.80486 

.95240 

.32144 

.94693 

.83792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.95749 

.30514 

.95231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222 

.82199 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.96204 

.32254 

.94656 

.83901 

.94078 

11 

60 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.82282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.83983 

.94049 

8 

53 

.27368 

.96182 

.29042 

.95690 

.30708 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96174 

.29070 

.95681 

.30736 

.95159 

.82392 

.94609 

.34038 

.94029 

55 

.27424 

.96166 

.29098 

.95673 

.30763 

.95150 

.32419 

.94599 

.34065 

.94019 

56 

.27452 

.96158 

.29126 

.95664 

.30791 

.95142 

.32447 

.94590 

.34093 

.94009 

57 

.27480 

.96150 

.29154 

.95656 

.30819 

.95133 

.82474 

.94580 

.34120 

.93999 

58 

.27508 

.96142 

.29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

59 

.27536 

.96134 

.29209 

.95639 

.30874 

.95115 

.82529 

.94561 

.34175 

.93979 

60 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

7 

1° 

?! 

5° 

75 

>° 

71 

0 

70 

0 

358 


MINE  GASES  AND  VENTILATION 


2 

0° 

2 

1° 

2 

2° 

2 

>o 

Z 

1° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.34202 

.93969 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

60 

1 

.34229 

.93959 

.35864 

.93348 

.37488 

.92707 

.39100 

.92039 

.40700 

.91S43 

69 

2 

.34257 

.93949 

.35891 

.93337 

.37515 

.92697 

.39127 

.92028 

.40727 

.91331 

58 

3 

.34284 

.93939 

.35918 

.93327 

.37542 

.92686 

.39153 

.92016 

.40753 

.91319 

57 

4 

.34311 

.93929 

.35945 

.93316 

.37569 

.92675 

.39180 

.92005 

.40780 

.91307 

56 

6 

.34339 

.93919 

.35973 

.93306 

.37595 

.92664 

.39207 

.91994 

.40806 

.91295 

55 

6 

.34366 

.93909 

.36000 

.93295 

.37622 

.92653 

.39234 

.91982 

.40833 

.91283 

54 

7 

.34393 

.93899 

.36027 

.93285 

.37649 

.92642 

.39260 

.91971 

.40860 

.91272 

53 

8 

.34421 

.93889 

.36054 

.93274 

.37676 

.92631 

.39287 

.91959 

.40886 

.91260 

52 

9 

.34448 

.93879 

.36081 

.93264 

.37703 

.92620 

.39314 

.91948 

.40913 

.91248 

61 

10 

.34475 

.93869 

.36108 

.93253 

.37730 

.92609 

.39341 

.91936 

.40939 

.91236 

50 

11 

.34503 

.93859 

.36135 

.93243 

.37757 

.92598 

.39367 

.91925 

.40966 

.91224 

49 

12 

.34530 

.93849 

.36162 

.93232 

.37784 

.92587 

.39394 

.91914 

.40992 

.91212 

48 

13 

.84557 

.93839 

.36190 

.93222 

.37811 

.92576 

.39421 

.91902 

.41019 

.91200 

47 

14 

.34584 

.93829 

.36217 

.93211 

.37838 

.92565 

.39448 

.91891 

.41045 

.91188 

46 

15 

.34612 

.93819 

.36244 

.93201 

.37865 

.92554 

.39474 

.91879 

.41072 

.91176 

45 

16 

.34639 

.93809 

.36271 

.93190 

.37892 

.92543 

.39501 

.91868 

.41098 

.91164 

44 

17 

.34666 

.93799 

.36298 

.93180 

.37919 

.92532 

.39528 

.91856 

.41125 

.91152 

43 

18 

.34694 

.93789 

.36325 

.93169 

.37946 

.92521 

.39555 

.91845 

.41151 

.91140 

42 

19 

.34721 

.93779 

.36352 

.93159 

.37973 

.92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

.34748 

.93769 

.36379 

.93148 

.37999 

.92499 

.39608 

.91822 

.41204 

.91116 

40 

21 

.34775 

.93759 

.36406 

.93137 

.38026 

.92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

.34803 

.93748 

.36434 

.93127 

.38053 

.92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

.34830 

.93738 

.36461 

.93116 

.38080 

.92466 

.39688 

.91787 

.41284 

.91080 

37 

24' 

.34857 

.93728 

.36488 

.93106 

.38107 

.92455 

.39715 

.91775 

.41310 

.91068 

86 

25 

.34884 

.93718 

.36515 

.93095 

.38134 

.92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

.34912 

.93708 

.36542 

.93084 

.38161 

.92432 

.39768 

.91752 

.41363 

.91044 

34 

27 

.34939 

.93698 

.36569 

.93074 

.38188 

.92421 

.39795 

.91741 

.41390 

.91032 

33 

28 

.34966 

.93688 

.36596 

.93063 

.38215 

.92410 

.39822 

.91729 

.41416 

.91020 

82 

29 

.34993 

.93677 

.36623 

.93052 

.38241 

.92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

.35021 

.93667 

.36650 

.93042 

.38268 

.92388 

.39875 

.91706 

.41469 

.90996 

30 

81 

.35048 

.93657 

.36677 

.93031 

.38295 

.92377 

.39902 

.91694 

.414% 

.90984 

29 

32 

.35075 

.93647 

.36704 

.93020 

.38322 

.92366 

.39928 

.91683 

.41522 

.90972 

28 

33 

.35102 

.93637 

.36731 

.93010 

.38349 

.92355 

.39955 

.91671 

.41549 

.90960 

27 

34 

.35130 

.93626 

.36758 

.92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

.35157 

.93616 

.36785 

.92988 

.38403 

.92332 

.40008 

.91648 

.41602 

.90936 

25 

36 

.35184 

.93606 

.36812 

.92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

.35211 

.93596 

.36839 

.92967 

.38456 

.92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

.35239 

.93585 

.36867 

.92956 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

.35266 

.93575 

.36894 

.92945 

.38510 

.92287 

.40115 

.91601 

.41707 

.90887 

21 

40 

.35293 

.93565 

.36921 

.92935 

.38537 

.92276 

.40141 

.91590 

.41734 

.90875 

20 

41 

.35320 

.93555 

.86948 

.92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.90863 

19 

42 

.35347 

.93544 

.36975 

.92913 

.38581 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

43 

.35375 

.93534 

.37002 

.92902 

.38617 

.92243 

.40221 

.91555 

.41813 

.90839 

17 

44 

.35402 

.93524 

.37029 

.92892 

.38644 

.92231 

.40248 

.91543 

.41840 

.90826 

16 

45 

.35429 

.93514 

.37056 

.92881 

.38671 

.92220 

.40275 

.91531 

.41866 

.90814 

15 

46 

.35456 

.93502 

.37083 

.92870 

.38698 

.92209 

.40301 

.91519 

.41892 

.90802 

14 

47 

.35484 

.93493 

.37110 

.92859 

.38725 

.92198 

.40328 

.91508 

.41919 

.90790 

13 

48 

.35511 

.93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945 

.90778 

12 

49 

.35538 

.93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972 

.90766 

11 

50 

.35565 

.93462 

.37191 

.92827 

.38805 

.92164 

.40408 

.91472 

.41998 

.90753. 

10 

51 

.35592 

.93452 

.87218 

.92816 

.88832 

.92152 

.40434 

.91461 

.42024 

.90741 

9 

52 

.35619 

.93441 

.37245 

.92805 

.38859 

.92141 

.40461 

.91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886 

.92130 

.40488 

.91437 

.42077 

.90717 

54 

.35674 

.93420 

.37299 

.92784 

.38912 

.92119 

.40514 

.91425 

.42104 

.90704 

65 

.35701 

.93410 

.37326 

.92773 

.38939 

.92107 

.40541 

.91414 

.42130 

.90692 

56 

.35728 

.93400 

.37353 

.92762 

.38966 

.920% 

.40567 

.91402 

.42156 

.90680 

57 

.35755 

.93389 

.37380 

.92751 

.38993 

.92085 

.40594 

.91390 

.42183 

.90668 

58 

.35782 

.93379 

.37407 

.92740 

.39020 

.92073 

.40621 

.91378 

.42209 

.90655 

59 

.35810 

.93368 

.37434 

.92729 

.39046 

.92062 

.40647 

.91366 

.42235 

.90643 

60 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

.42262 

.90631 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

t 

6< 

>° 

6J 

o 

61 

0 

66 

0 

65 

0 

/ 

SINES  AND  COSINES 


359 


25° 


.42262 
.42288 
.42315 
.42341 
.42367 
.42394 
.42420 
.42446 
.42473 
.42499 
.42525 

.42552 
.42578 
.42604 
.42631 
.42657 
.42683 
.42709 
.42736 
.42762 
.42788 

.42815 
.42841 
.42867 
.42894 
.42920 
.42946 
.42972 
.42999 
.43025 
.43051 

.43077 
.43104 
.43130 
.43156 
.43182 
.43209 
.43235, 
.43261 
.43287 
.43313 

.43340 
.43366 
.43392 
.43418 


.43497 
.43523 
.43549 
.43575 

.43602 
.43628 
.43654 
.43680 
.43706 
.43733 
.43759 
.43785 
.43811 
.43837 


.90631 
.90618 
.90606 
.90594 


.90557 
.90545 
.90532 
.90520 
.90507 

.90495 
.90483 
.90470 
.90458 
.90446 
.90433 
.90421 


.90371 
.90358 
.90346 
.90334 
.90321 
.90309 
.90296 
.90284 
.90271 
.90259 

.90246 
.90233 
.90221 
.90208 
.90196 
.90183 
.90171 
.90158 
.90146 
.90133 

.90120 
.90108 
.90095 
.90082 
.90070 
.90057 
.90045 
.90032 
.90019 
.90007 


.89956 
.89943 
.89930 
.89918 
.89905 
.89892 


Coilne      Sine 


64° 


.43837 
.43863 
.43889 
.43916 
.43942 
.43968 
.43994 
.44020 
.44046 
.44072 


.44124 
.44151 
.44177 
.44203 
.44229 
.44255 
.44281 
.44307 
.44333 
.44359 

.44385 
.44411 
.44437 
.44464 
.44490 
.44516 
.44542 
.44568 
.44594 
.44620 

.44646 

.44672 
.44698 
.44724 
.44750 
.44776 
.44802 
.44828 
.44854 
.44880 

.44906 
.44932 
.44958 
.44984 
.45010 
.45036 
.45062 
.45088 
.45114 
.45140 

.45166 
.45192 
.45218 
.45243 
.45269 
.45295 
.45321 
.45347 
.45373 
.45399 


.89879 
.89867 
.89854 
.89841 
.89828 
.89816 
.89803 
.89790 
.89777 
.89764 
.89752 

.89739 
.89726 
.89713 
.89700 


.89610 
.89597 
.89584 
.89571 
.89558 
.89545 
.89532 
.89519 
.89506 
.89493 


.89467 
.89454 
.89441 


.89285 
.89272 


.89219 
.89206 
.89193 


.89127 
.89114 
.89101 


Cosine       Sine 


63° 


27° 


.45399 
.45425 
.45451 
.45477 
.45503 
.45529 
.45554 
.45580 
.45606 
.45632 
.45658 

.45684 
.45710 
.45736 
.45762 
.45787 
.45813 
.45839 
.45865 
.45891 
.45917 

.45942 
.45968 
.45994 
.46020 
.46046 
.46072 
.46097 
.46123 
.40149 
.46175 

.46201 

.46226 
.46252 
.46278 
.46304 
.46330 
.46355 
.46381 
.46407 
.46433 

.46458 
.46484 
.46510 
.46536 
.46561 
.46587 
.46613 
.46639 
.46664 


.46716 
.46742 
.46767 
.46793 
.46819 
.46844 
.46870 
.46896 
.46921 
.46947 


Cosine       Sine 


G2° 


Sine       Cosine 


.46947 
.46973 
.46999 
.47024 
.47050 
.47076 
.47101 
.47127 
.47153 
.47178 
.47204 

.47229 
.47255 
.47281 
.47306 
.47332 
.47358 
.47383 
.47409 
.47434 
.47460 

.47486 
.47511 
.47537 
.47562 
.47588 
.47614 
.47639 
.47665 
.47690 
.47716 

.47741 
.47767 
.47793 

.47818 
.47844 


.47895 
.47920 
.47946 
.47971 

.47997 

.48022 
.48048 
.48073 
.48099 
.48124 
.48150 
.48175 
.48201 


.48252 
.48277 
.48303 
.48328 
.48354 
.48379 
.48405 
.48430 
.48456 
.48481 


.88254 
.88240 


.88199 
.88185 
.88172 
.88158 

.88144 


.88006 
.87993 
.87979 
.87965 
.87951 
.87937 
.87923 


.87854 
.87840 
.87826 
.87812 
.87798 
.87784 
.87770 
.87756 
.87743 

.87729 
.87715 
.87701 
.87687 
.87673 
.87659 
.87645 
.87631 
.87617 
.87603 


.87575 
.87561 
.87546 
.87532 
.87518 
.87504 
.87490 
.87476 
.87462 


Cosine       Sine 


61° 


29° 


Sine      Conine 


.48481 
.48506 
.48532 
.48557 


.48684 
.48710 
.48735 

.48761 

.48786 
.48811 
.48837 
.48862 
.48888 
.48913 
.48938 
.48964 


.49014 
.49040 
.49065 
.49090 
.49116 
.49141 
.49160 
.49192 
.49217 
.4C242 


.49293 
.49318 
.49344 
.49369 
.49394 
.49419 
.49445 
.49470 
.49495 

.49521 
.49546 
.49571 
.49596 
.49622 
.49647 
.49672 
.49697 
.49723 
.49748 

.49773 
.49798 
.49824 
.49849 
.49874 
.49899 
.49924 
.49950 
.49975 
.50000 


.87462 
.87448 
.87434 
.87420 
.87406 
.87391 
.87377 
.87363 


.87292 
.87278 
.87264 
.87250 
.87235 
.87221 


.87164 
.87150 


.87121 
.87107 


.87050 
.87036 


.87021 
.87007 


.86791 
.86777 
.86762 


.86719 
.86704 


.86661 
.86646 
.86632 
.86617 
.86603 


Cosine   Si 


60° 


3(30 


MINE  GASES  AND   VENTILATION 


3< 

J° 

3 

P 

3' 

20 

3 

5° 

34 

0 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

.50000 

.86603 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

60 

.50025 

.86588 

.51529 

.85702 

.53017 

.84789 

.54488 

.83851 

.55943 

.82887 

59 

.50050 

.86573 

.51554 

.85687 

.53041 

.84774 

.54513 

.83835 

.55968 

.82871 

68 

.50076 

.86559 

.51579 

.85672 

.53066 

.84759 

.54537 

.83819 

.55992 

.82855 

67 

.50101 

.86544 

.51604 

.85657 

.53091 

.84743 

.54561 

.83804 

.56016 

.82839 

66 

.50126 

.86530 

.51628 

.85642 

.53115 

.84728 

.54586 

.83788 

.56040 

.82822 

65 

.50151 

.86515 

.51653 

.85627 

.53140 

.84712 

.54610 

.83772 

.56064 

.82806 

54 

.50176 

.86501 

.51678 

.85612 

.53164 

.84697 

.54635 

.83756 

.56088 

.82790 

63 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659 

.83740 

.56112 

.82773 

62 

9 

.50227 

.86471 

.51728 

.85582 

.53214 

.84666 

.54683 

.83724 

.56136 

.82757 

61 

10 

.50252 

.86457 

.51753 

.85567 

.53238 

.84650 

.54708 

.83708 

.56160 

.82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

.84635 

.54732 

.83692 

.56184 

.82724 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83676 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51828 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82692 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.54805 

.83645 

.56256 

.82675 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.54829 

.83629 

.66280 

.82659 

45 

16 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.64854 

.83613 

.56305 

.82643 

44 

17 

.50428 

.86354 

.51927 

.85461 

.53411 

.84542 

.54878 

.83597 

.56329 

.82626 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84526 

.54902 

.83581 

.56353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53460 

.84511 

.54927 

.83565 

.56377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52026 

.85401 

.53509 

.84480 

.54975 

.83533 

.56425 

.82561 

39 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84464 

.54999 

.83517 

.66449 

.82544 

38 

23 

.50578 

.86266 

.52076 

.85370 

.53558 

.84448 

.55024 

.83501 

.66473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.84433 

.55048 

.83485 

.56497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83469 

.56521 

.82495 

35 

26 

.50654 

.86222 

.52151 

.85325 

.53632 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

27 

.50679 

.86207 

.52175 

.85310 

.53656 

.84386 

.55121 

.83437 

.  .56569 

.82462 

33 

28 

.50704 

.86192 

.52200 

.85294 

.53681 

.84370 

.55145 

.83421 

.56593 

.82446 

82 

29 

.50729 

.86178 

.52225 

.85279 

.53705 

.84355 

.55169 

.83405 

.56617 

.82429 

81 

30 

.50754 

.86163 

.52250 

.85264 

.53730 

.84339 

.65194 

.83389 

.56641 

.82413 

80 

31 

.50779 

.86148 

.52275 

.85249 

.53754 

.84324 

.65218 

.83373 

.56665 

.82396 

29 

32 

.50804 

.86133 

.52299 

.85234 

.53779 

.84308 

.65242 

.83356 

.56689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.55266 

.83340 

.56713 

.82363 

27 

34 

.50854 

.86104 

.52349 

.85203 

.53828 

.84277 

.65291 

.83324 

.56736 

.82347 

26 

35 

.50879 

.86089 

.52374 

.85188 

.53853 

.84261 

.55315 

.83308 

.56760 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.65339 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83276 

.56808 

.82297 

23 

88 

.50954 

.86045 

.52448 

.85142 

.53926 

.84214 

.55388 

.83260 

.56832 

.82281 

22 

39 

.50979 

.86030 

.52473 

.85127 

.53951 

.84198 

.55412 

.83244 

.66856 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112  . 

.53975 

.84182 

.65436 

.83228 

.56880 

.82248 

20 

41 

.51029 

.86000 

.52522 

.85096 

.54000 

.84167 

.55460 

.83212 

.56904 

.82281 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

18 

43 

.51079 

.85970 

.52572 

.85066 

.54049 

.84135 

.55509 

.83179 

.56952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051 

.54073 

.84120 

.55533 

.83163 

.56976 

.82181 

16 

45 

.51129 

.85941 

.52621 

.85035 

.54097 

.84104 

.55557 

.83147 

.57000 

.82165 

15 

46 

.51154 

.85926 

.52646 

.85020 

.54122 

.84088 

.55581 

.83131 

.57024 

.82148 

14 

47 

.51179 

.85911 

.52671 

.85005 

.54146 

.84072 

.55605 

.83115 

.57047 

.82132 

13 

48 

.51204 

.85896 

.52696 

.84989 

.54171 

.84057 

.55630 

.83098 

.57071 

.82115 

12 

49 

.51229 

.85881 

.52720 

.84974 

.54195 

.84041 

.55654 

.83082 

.57095 

.82098 

11 

50 

.51254 

.85866' 

.52745 

.84959 

.54220 

.84025 

.55678 

.83066 

.57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.55702 

.83050 

.57143 

.82065 

9 

52 

.51304 

.85836 

.52794 

.84928 

.54269 

.83994 

.55726 

.83034 

.57167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293 

.83978 

.55750 

.83017 

.57191 

.82032 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82015 

55 

.51379 

.85792 

.52869 

.84882 

.54342 

.83946 

.55799 

.82985 

.57238 

.81999 

56 

.51404 

.85777 

.52896 

.84866 

.54366 

.83930 

.55823 

.82969 

.57262 

.81982 

57 

.51429 

.85762 

.52918 

.84851 

.54391 

.83915 

.65847 

.82953 

.57286 

.81965 

58 

.51454 

.85747 

.62943 

.84836 

.54415 

.83899 

.55871 

.82936 

.57310 

.81949 

59 

.51479 

.85732 

.52967 

.84820 

.64440 

.83883 

.55895 

.82920 

.57334 

.81938 

60 

.51504 

.85717 

.52992 

.84805 

.64464 

.83867 

.55919 

.82904 

.57358 

181915 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

f 

Bf 

>° 

a 

5° 

5' 

JO  ' 

5( 

5° 

K 

o 

/ 

SINES  AND  COSINES 


361 


36° 

36° 

37° 

38° 

39° 

/ 

S,  ie 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.67358 

.81915 

.68779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

60 

.67381 

.81899 

.68802 

.80885 

.60205 

.79846 

.61589 

.78783 

.62956 

.77696 

69 

2 

.67405 

.81882 

.58826 

.80867 

.60228 

.79829 

.61612 

.78765 

.62977 

.77678 

58 

8 

.67429 

.81865 

.58849 

.80850 

.60251 

.79811 

.61635 

.78747 

.63000 

.77660 

57 

4 

.57453 

.81848 

.68873 

.80833 

.60274 

.79793 

.61658 

.78729 

.63022 

.77641 

66 

fi 

.67477 

.81832 

.68896 

.80816 

.60298 

.79776 

.61681 

.78711 

.63045 

.77623 

66 

6 

.67501 

.81815 

.58920 

.80799 

.60321 

.79758 

.61704 

.78694 

.63068 

.77605 

54 

7 

.67524 

.81798 

.68943 

.80782 

.60344 

.79741 

.61726 

.78676 

.63090 

.77586 

53 

8 

.67548 

.81782 

.68967 

.80765 

.60367 

.79723 

.61749 

.78658 

.63113 

.77568 

52 

9 

.67572 

.81765 

.68990 

.80748 

.60390 

.79706 

.61772 

.78640 

.63135 

.77550 

51 

10 

.57596 

.81748 

.59014 

.80730 

.60414 

.79688 

.61795 

.78622 

.63158 

.77531 

50 

11 

.67619 

.81731 

.69037 

.80718 

.60437 

.79671 

.61818 

.78604 

.63180 

.77518 

49 

12 

.67643 

.81714 

.69061 

.80696 

.60460 

.79653 

.61841 

.78586 

.63203 

.77494 

48 

13 

.67667 

.81698 

.69084 

.80679 

.60483 

.79635 

.61864 

.78568 

.63225 

.77476 

47 

14 

.67691 

.81681 

.69108 

.80662 

.60506 

.79618 

.61887 

.78550 

.63248 

.77458 

46 

15 

.57715 

.81664 

.59131 

.80644 

.60529 

.79600 

.61909 

.78532 

.63271 

.77439 

45 

16 

.67738 

.81647 

.59154 

.80627 

.60553 

.79583 

.61932 

.78514 

.63293 

.77421 

44 

17 

.57762 

.81631 

.69178 

.80610 

.60576 

.79565 

.61955 

.78496 

.63316 

.77402 

43 

18 

.57786 

.81614 

.59201 

.80593 

.60599 

.79547 

.61978 

.78478 

.63338 

.77384 

42 

19 

.57810 

.81597 

.59225 

.80576 

.60622 

.79530 

.62001 

.78460 

.63361 

.77366 

41 

20 

.57833 

.81580 

.59248 

.80558 

.60645 

.79512 

.62024 

.78442 

.63383 

.77347 

40 

21 

.57857 

.81563 

.69272 

.80541 

.60668 

.79494 

.62046 

.78424 

.63406 

.77329 

39 

22 

.57881 

.81546 

.69295 

.80524 

.60691 

.79477 

.62069 

.78405 

.63428 

.77310 

38 

23 

.57904 

.81530 

.59318 

.80507 

.60714 

.79459 

.62092 

.78387 

.63451 

.77292 

37 

24 

.57928 

.81513 

.59342 

.80489 

.60738 

.79441 

.62115 

.78369 

.63473 

.77273 

36 

25 

.57952 

.81496 

.59365 

.80472 

.60761 

.79424 

.62138 

.78351 

.63496 

.77255 

35 

26 

.57976 

.81479 

.59389 

.80455 

.60784 

.79406 

.62160 

.78333 

.63518 

.77236 

34 

27 

.57999 

.81462 

.69412 

.80438 

.60807 

.79388 

.62183 

.78315 

.63540 

.77218 

33 

28 

.68023 

.81445 

.59436 

.80420 

.60830 

.79371 

.62206 

.78297 

.63563 

.77199 

32 

29 

.58047 

.81428 

.59459 

.80403 

.60853 

.79353 

.62229 

.78279 

.63585 

.77181 

31 

SO 

.58070 

.81412 

.59482 

.80386 

.60876 

.79335 

.62251 

.78261 

.63608 

.77162 

30 

81 

.58094 

.81395 

.59506 

.80368 

.60899 

.79318 

.62274 

.78243 

.63630 

.77144 

29 

82 

.58118 

.81378 

.69529 

.80351 

.60922 

.79300 

.62297 

.78225 

.63653 

.77125 

28 

83 

.58141 

.81361 

.59552 

.80334 

.60945 

.79282 

.62320 

.78206 

.63675 

.77107 

27 

34 

.58165 

.81344 

.59576 

.80316 

.60968 

.79264 

.62342 

.78188 

.63698 

.77088 

26 

35 

.58189 

.81327 

.59599 

.80299 

.60991 

.79247 

.62365 

.78170 

.63720 

.77070 

25 

36 

.58212 

.81310 

.59622 

.80282 

.61015 

.79229 

.62388 

.78152 

.63742 

.77061 

24 

37 

.58236 

.81293 

.59646 

.80264 

.61038 

.79211 

.62411 

.78134 

.63765 

.77033 

23 

38 

.58260 

.81276 

.59669 

.80247 

.61061 

.79193 

.62433 

.781  10 

.63787 

.77014 

22 

39 

.58283 

.81259 

.59693 

.80230 

.61084 

.79176 

.62456 

.78098 

.63810 

.76996 

21 

40 

.68307 

.81242 

.59716 

.80212 

.61107 

.79158 

.62479 

.78079 

.63832 

.76977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.61130 

.79140 

.62502 

.78061 

.63854 

.76959 

19 

42 

.68354 

.81208 

.59763 

.80178 

.61153 

.79122 

.62524 

.78043 

.63877 

.76940 

18 

43 

.68378 

.81191 

.69786 

.80160 

.61176 

.79105 

.62547 

.78025 

.63899 

.76921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.61199 

.79087 

.62570 

.78007 

.63922 

.76903 

16 

45 

.58425 

.81157 

.59832 

.80125 

.61222 

.79069 

.62592 

.77988 

.63944 

.76884 

15 

46 

.58449 

.81140 

.59856 

.80108 

.61245 

.79051 

.62615 

.77970 

.63966 

.76866 

14 

47 

.68472 

.81123 

.59879 

.80091 

.61268 

.79033 

.62638 

.77952 

.63989 

.76847 

13 

48 

.58496 

.81106 

.59902 

.80073 

.61291 

.79016 

.62660 

.77934 

.64011 

.76828 

12 

49 

.58519 

.81089 

.69926 

.80056 

.61314 

.78998 

.62683 

.77916 

.64033 

.76810 

11 

50 

.68543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879 

.64078 

.76772 

9 

52 

.68590 

.81038 

.59995 

.80003 

.61383 

.78944 

.62751 

.77861 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986 

.61406 

.78926 

.62774 

.77843 

.64123 

.76735 

7 

64 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.58661 

.80987 

.60065 

.79951 

.61451 

.78891 

.62819 

.77806 

.64167 

.76698 

5 

56 

.58684 

.80970 

.60089 

.79934 

.61474 

.78873 

.62842 

.77788 

.64190 

.76679 

4 

67 

.58708 

.80953 

.60112 

.79916 

.61497 

.78855 

.62864 

.77769 

.64212 

.76661 

8 

58 

.58731 

.80936 

.60135 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.76642 

2 

59 

.58755 

.80919 

.60158 

.79881 

.61548 

.78819 

.62909 

.77733 

.64256 

.76623 

1 

60 

.68779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

.64279 

.76604 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

54° 

53° 

52° 

51° 

50° 

/ 

362 


MINE  GASES  AND   VENTILATION 


4 

v> 

4 

L° 

45 

J° 

4, 

J° 

44 

0 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.64279 

.76604 

.65606 

.75471 

.66913 

.74314 

.68200 

.73135 

.69466 

.71934 

60 

1 

.64301 

.76586 

.65628 

.75452 

.66935 

.74295 

.68221 

.73116 

.69487 

.71914 

59 

2 

.64323 

.76567 

.65650 

.75433 

.66956 

.74276 

.68242 

.73096 

.69508 

.71894 

58 

3 

.64346 

.76548 

.65672 

.75414 

.66978 

.74256 

.68264 

.73076 

.69529 

.71873 

57 

4 

.64368 

.76530 

.65694 

.75395 

.66999 

.74237 

.68285 

.73056 

.69549 

.71853 

56 

5 

.64390 

.76511 

.65716 

.75375 

.67021 

.74217 

.68306 

.73036 

.69570 

.71833 

55 

6 

.64412 

.76492 

.65738 

.75356 

.67043 

.74198 

.68327 

.73016 

.69591 

.71813 

54 

7 

.64435 

.76473 

.65759 

.75337 

.67064 

.74178 

.68349 

.72996 

.69612 

.71792 

53 

8 

.64457 

.76455 

.65781 

.75318 

.67086 

.74159 

.68370 

.72976 

.69633 

.71772 

52 

9 

.64479 

.76436 

.65803 

.75299 

.67107 

.74139 

.68391 

.72957 

.69654 

.71752 

51 

10 

.64501 

.76417 

.65825 

.75280 

.67129 

.74120 

.68412 

.72937 

.69675 

.71732 

50 

11 

.64524 

.76398 

.65847 

.75261 

.67151 

.74100 

.68434 

.72917 

.69696 

.71711 

49 

12 

.64546 

.76380 

.65869 

.75241 

.67172 

.74080 

.68455 

.72897 

.69717 

.71691 

48 

13 

.64568 

.76361 

.65891 

.75222 

.67194 

.74061 

.68476 

.72877 

.69737 

.71671 

47 

14 

.64590 

.76342 

.65913 

.75203 

.67215 

.74041 

.68497 

.72857 

.69758 

.71650 

46 

15 

.64612 

.76323 

.65935 

.75184 

.67237 

.74022 

.68518 

.72837 

.69779 

.71630 

45 

16 

.64635 

.76304 

.65956 

.75165 

.67258 

.74002 

.68539 

.72817 

.69800 

.71610 

44 

17 

.64657 

.76286 

.65978 

.75146 

.67280 

.73983 

.68561 

.72797 

.69821 

.71590 

43 

18 

.64679 

.76267 

.66000 

.75126 

.67301 

.73963 

.68582 

.72777 

.69842 

.71569 

42 

19 

.64701 

.76248 

.66022 

.75107 

.67323 

.73944 

.68603 

.72757 

.69862 

.71549 

41 

20 

.64723 

.76229 

.66044 

.75088 

.67344 

.73924 

.68624 

.72737 

.69883 

.71529 

40 

21 

.64746 

.76210 

.66066 

.75069 

.67366 

.73904 

.68645 

.72717 

.69904 

.71508 

39 

22 

.64768 

.76192 

.66088 

.75050 

.67387 

.73885 

.68666 

.72697 

.69925 

.71488 

38 

23 

.64790 

.76173 

.66109 

.75030 

.67409 

.73865 

.68688 

.72677 

.69946 

.71468 

37 

24 

.64812 

.76154 

.66131 

.75011 

.67430 

.73846 

.68709 

.72657 

.69966 

.71447 

36 

35 

.64834 

.76135 

.66153 

.74992 

.67452 

.73826 

.68730 

.72637 

.69987 

.71427 

35 

26 

.64856 

.76116 

.66175 

.74973 

.67473 

.73806 

.68751 

.72617 

.70008 

.71407 

34 

27 

.64878 

.76097 

.66197 

.74953 

.67495 

.73787 

.68772 

.72597 

.70029 

.71386 

33 

26 

.64901 

.76078 

.66218 

.74934 

.67516 

.73767 

.68793 

.72577 

.70049 

.71366 

32 

29 

.64923 

.76059 

.66240 

.74915 

.67538 

.73747 

.68814 

.72557 

.70070 

.71345 

31 

30 

.64945 

.76041 

.66262 

.74896 

.67559 

.73728 

.68835 

.72537 

.70091 

.71325 

30 

31 

.64967 

.76022 

.66284 

.74876 

.67580 

.73708 

.68857 

.72517 

.70112 

.71305 

29 

82 

.64989 

.76003 

.66306 

.74857 

.67602 

.73688 

.68878 

.72497 

.70132 

.71284 

28 

33 

.65011 

.75984 

.66327 

.74838 

.67623 

.73669 

.68899 

.72477 

,70153 

.71264 

27 

34 

.65033 

.75965 

.66349 

.74818 

.67645 

.73649 

.68920 

.72457 

.70174 

.71243 

26 

35 

.65055 

.75946 

.66371 

.74799 

.67666 

.73629 

.68941 

.72437 

.70195 

.71223 

25 

36 

.65077 

.75927 

.66393 

.74780 

.67688 

.73610 

.68962 

.72417 

.70215 

.71203 

24 

87 

.65100 

.75908 

.66414 

.74760 

.67709 

.73590 

.68983 

.72397 

.70236 

.71182 

29 

38 

.65122 

.75889 

,66436 

.74741 

.67730 

.73570 

.69004 

.72377 

.70257 

.71162 

2> 

89 

.65144 

.75870 

.66458 

.74722 

.67752 

.73551 

.69025 

.72357 

.70277 

.71141 

21 

40 

.65166 

.75851 

.66480 

.74703 

.67773 

.73531 

.69046 

.72337 

.70298 

.71121 

20 

41 

.65188 

.75832 

.66501 

.74683 

.67795 

.73511 

.69067 

.72317 

.70319 

.71100 

19 

42 

.65210 

.75813 

.66523 

.74664 

.67816 

.73491 

.69088 

.72297 

.70339 

.71080 

18 

43 

.65232 

.75794 

.66545 

.74644 

.67837 

.73472 

.69109 

.72277 

.70360 

.71059 

11 

44 

.65254 

.75775 

.66566 

.74625 

.67859 

.73452 

.69130 

.72257 

.70381 

.71039 

1C 

45 

.65276 

.75756 

.66588 

.74606 

.67880 

.73432 

.69151 

.72236 

.70401 

.71019 

15 

46 

.65298 

.75738 

.66610 

.74586 

.67901 

.73413 

.69172 

.72216 

.70422 

.70998 

14 

47 

.65320 

.75719 

.66632 

.74567 

.67923 

.73393 

.69193 

.72196 

.70443 

.70978 

1* 

48 

.65342 

.75700 

.66653 

.74548 

.67944 

.73373 

.69214 

.72176 

.70463 

.70957 

11 

49 

.65364 

.75680 

*66675 

.74528 

.67965 

.73353 

.69235 

.72156 

.70484 

.70937 

11 

50 

.65386 

.75661 

.66697 

.74509 

.67987 

.73333 

.69256 

.72136 

.70505 

.70916 

10 

51 

.65408 

.75642 

.66718 

.74489 

.68008 

.73314 

.69277 

.72116 

.70525 

.70896 

52 

.65430 

.75623 

.66740 

.74470 

.68029 

.73294 

.69298 

.72095 

.70546 

.70875 

53 

.65452 

.75604 

.66762 

.74451 

.68051 

.73274 

.69319 

.72075 

.70567 

.70856 

54 

.65474 

.75585 

.66783 

.74431 

.68072 

.73254 

.69340 

.72055 

.70587 

.70834 

55 

.65496 

.75566 

.66805 

.74412 

.68093 

.73234 

.69361 

.72035 

.70608 

.70813 

56 

.65518 

.75547 

.66827 

.74392 

.68115 

.73215 

.69382 

.72015 

.70628 

.70793 

57 

.65540 

.75528 

.66848 

.74373 

.68136 

.73195 

.69403 

.71995 

.70649 

.70772 

58 

.65562 

.75509 

.66870 

.74353 

.68157 

.73175 

.69424 

.71974 

.70670 

.70752 

59 

.65584 

.75490 

.66891 

.74334 

.68179 

.73155 

.69445 

.71954 

.70690 

.70781 

60 

.65606 

.75471 

.66913 

.74314 

.68200 

.73135 

.69466 

.71934 

.70711 

.70711 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

4 

9° 

4J 

S° 

4' 

?o 

4 

i° 

4£ 

0 

r 

TANGENTS  AND  COTANGENTS 


304 


MINE  GASES  AND  VENTILATION 


f 

Of 

» 

1 

3 

2* 

j 

3 

9 

4 

» 

Twig 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infill. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

60 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

.07022 

14.2411 

59 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

.07051 

14.1821 

58 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.9372 

.05328 

18.7678 

.07080 

14.1235 

57 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

.07110 

14.0655 

56 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

.07139 

14.0079 

55 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

.07168 

13.9507 

54 

.00204 

491.106 

.01949 

51.3032 

.03696 

27.0566 

.05445 

18.3655 

.07197 

13.8940 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

.07227 

13.8378 

52 

9 

.00232 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

.07256 

13.7821 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

.07285 

13.7267 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05562 

17.9802 

.07314 

13.6719 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

.07344 

13.6174 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

.07373 

13.5634 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

.07402 

13.5098 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

.07431 

13.4566 

45 

16 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

.07461 

13.4039 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

.07490 

13.3515 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.8978 

.05766 

17.3432 

.07519 

13.2996 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24.7185 

.05795 

17.2558 

.07548 

13.2480 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

.07578 

13.1969 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

.07607 

13.1461 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

.07636 

13.0958 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

.07665 

13.0458 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

.07695 

12.S962 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

.07724 

12.9469 

35 

20 

.00756 

132.219 

.02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

.07753 

12.8981 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

.07782 

12.8496 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.04308 

23.2137 

.06058 

16.5075 

.07812 

12.8014 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

.07841 

12.7536 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

.07870 

12.7062 

30 

31 

.00902 

110.892 

.0?,648 

97.7686 

.04395 

22.7519 

.06145 

16.2722 

.07899 

12.6591 

29 

32 

.00931 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

.07929 

12.6124 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.06204 

16.1190 

.07958 

12.5660 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

.OT987 

12.5199 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.06262 

15.9687 

.08017 

12.4742 

25 

36 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

.08046 

12.4288 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

.08075 

12.3838 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

.08104 

12.3390 

22 

39 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

.08134 

12.2946 

21 

40 

.01164 

85.9398 

.02910 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

.08163 

12-.2505 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.8369 

.06437 

15.5340 

.08192 

12.2067 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21.2049 

.06467 

15.4638 

.08221 

12.1632 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

.08251 

12.1201 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

.08280 

12.0772 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

.08309 

12.0346 

15 

46 

.01338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

.08339 

11.9923 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

.08368 

11.9504 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

.08397 

11.9087 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

.08427 

11.8673 

11 

50 

.01455 

68.7501 

.03201 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

.08456 

11.8262 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

.08485 

11.7853 

52 

.01513 

66.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

.08514 

11.7448 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

.08544 

11.7045 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

.08573 

11.6645 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

.08602 

11.6248 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

.08632 

11.5853 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

.08661 

11.5461 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

.08690 

11.5072 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

.08720 

11.4685 

60 

.01748 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

.08749 

11.4301 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

8 

9° 

8 

8° 

8 

7° 

8 

6° 

8 

5° 

TANGENTS  AND  COTANGENTS 


365 


5 

o  . 

6 

S 

D 

8 

3 

9 

- 

Tan<T 

Cotan" 

TttTlW 

Tftn<* 

Cotang 

o  ang 

i  an0 

>  ang 

l  atl0 

.08749 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

60 

.08778 

11.3919 

.10540 

9.48781 

.12308 

8.12481 

.14084 

7.10038 

.15868 

6.30189 

59 

.08807 

11.3540 

.10569 

9.46141 

.12338 

8.10536 

.14113 

7.08546 

.15898 

6.29007 

58 

.08837 

11.3163 

.10599 

9.43515 

.12367 

8.08600 

.14143 

7.07059 

.15928 

6.27829 

57 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06674 

.14173 

7.05579 

.15958 

6.26655 

56 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04756 

.14202 

7.04105 

.15988 

6.25486 

55 

.08925 

11.2048 

.10687 

9.35724 

.12456 

8.02848 

.14232 

7.02637 

.16017 

6.24321 

54 

.08954 

11.1681 

.10716 

9.33155 

.12485 

8.00948 

.14262 

7.01174 

.16047 

6.23160 

53 

.08983 

11.1316 

.10746 

9.30599 

.12515 

7.99058 

.14291 

6.99718 

.16077 

6.22003 

52 

.09013 

11.0954 

.10775 

9.28058 

.12544 

7.97176 

.14321 

6.98268 

.16107 

6.20851 

51 

10 

.09042 

11.0594 

.10805 

9.25530 

.12574 

7.95302 

.14351 

6.96823 

.16137 

6.19703 

50 

11 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

.14381 

6.95385 

.16167 

6.18559 

49 

12 

.09101 

10.9882 

.10863 

9.20516 

.12633 

7.91582 

.14410 

6.93952 

.16196 

6.17419 

48 

13 

.09130 

10.9529 

.10893 

9.18028 

.12662 

7.89734 

.14440 

6.92525 

.16226 

6.16283 

47 

14 

.09159 

10.9178 

.10922 

9.15554 

.12692 

7.87895 

.14470 

6.91104 

.16256 

6.15151 

46 

15 

.09189 

10.8829 

.10952 

9.13093 

.12722 

7.86064 

.14499 

6.89688 

.16286 

6.14023 

45 

16 

.09218 

10.8483 

.10981 

9.10646 

.12751 

7.84242 

.14529 

6.88278 

.16316 

6.12899 

44 

17 

.09247 

10.8139 

.11011 

9.08211 

.12781 

7.82428 

.14559 

6.86874 

.16346 

6.11779 

43 

18 

.09277 

10.7797 

.11040 

9.05789 

.12810 

7.80622 

.14588 

6.85475 

.16376 

6.10664 

42 

19 

.09306 

10.7457 

.11070 

9.03379 

.12840 

7.78825 

.14618 

6.84082 

.16405 

6.09552 

41 

20 

.09335 

10.7119 

.11099 

9.00983 

.12869 

7.77035 

.14648 

6.82694 

.16435 

6.08444 

40 

21 

.09365 

10.6783 

.11128 

8.98598 

.12899 

7.75254 

.14678 

6.81312 

.16465 

6.07340 

39 

22 

.09394 

10.6450 

.11158 

8.96227 

.12929 

7.73480 

.14707 

6.79936 

.16495 

6.06240 

38 

23 

.09423 

10.6118 

.11187 

8.93867 

.12958 

7.71715 

.14737 

6.78564 

.16525 

6.05143 

37 

24 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.69957 

.14767 

6.77199 

.16555 

6.04051 

36 

25 

.09482 

10.5462 

.11246 

8.89185 

.13017 

7.68208 

.14796 

6.75838 

.16585 

6.02962 

35 

26 

.09511 

10.5136 

.11276 

8.86862 

.13047 

7.66466 

.14826 

6.74483 

.16615 

6.01878 

34 

27 

.09541 

10.4813 

.11305 

8.84551 

.13076 

7.64732 

.14856 

6.73133 

.16645 

6.00797 

33 

28 

.09570 

10.4491 

.11335 

8.82252 

.13106 

7.63005 

.14886 

6.71789 

.16674 

5.99720 

32 

29 

.09600 

10.4172 

.11364 

8.79964 

.13136 

7.61287 

.14915 

6.70450 

.16704 

5.98646 

31 

30 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

.14945 

6.69116 

.16734 

5.97576 

30 

31 

.09658 

10.3538 

.11423 

8.75425 

.13195 

7.57872 

.14975 

6.67787 

.16764 

5.96510 

29 

32 

.09688 

10.3224 

.11452 

8.73172 

.13224 

7.56176 

.15005 

6.66463 

.16794 

5.95448 

28 

33 

.09717 

10.2913 

.11482 

8.70931 

.13254 

7.54487 

.15034 

6.65144 

.16824 

5.94390 

27 

34 

.09746 

10.2602 

.11511 

8.68701 

.13284 

7.52806 

.15064 

6.63831 

.16854 

5.93335 

26 

35 

.09776 

10.2294 

.11541 

8.66482 

.13313 

7.51132 

.15094 

6.62523 

.16884 

5.92283 

25 

36 

.09805 

10.1988 

.11570 

8.64275 

.13343 

7.49465 

.15124 

6.61219 

.16914 

5.91236 

24 

37 

.09834 

10.1683 

.11600 

8.62078 

.13372 

7.47806 

.15153 

6.59921 

.16944 

5.90191 

23 

38 

.09864 

10.1381 

.11629 

8.59893 

.13402 

7.46154 

.15183 

6.58627 

.16974 

5.89151 

22 

39 

.09893 

10.1080 

.11659 

8.57718 

.13432 

7.44509 

.15213 

6.57339 

.17004 

5.88114 

21 

40 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

.15243 

6.56055 

.17033 

5.87080 

20 

41 

.09952 

10.0483 

.11718 

8.53402 

.13491 

7.41240 

.15272 

6.54777 

.17063 

5.86051 

19 

42 

.09981 

10.0187 

.11747 

8.51259 

.13521 

7.39616 

.15302 

6.53503 

.17093 

5.85024 

18 

43 

.10011 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

.15332 

6.52234 

.17123 

5.84001 

17 

44 

.10040 

9.96007 

.11806 

8.47007 

.13580 

7.36389 

.15362 

6.50970 

.17153 

5.82982 

16 

45 

.10069 

9.93101 

.11836 

8.44896 

.13609 

7.34786 

.15391 

6.49710 

.17183 

5.81966 

15 

46 

.10099 

9.90211 

.11865 

8.42795 

.13639 

7.33190 

.15421 

6.48456 

.17213 

5.80953 

14 

47 

.10128 

9.87338 

.11895 

8.40705 

.13669 

7.31600 

.15451 

6.47206 

.17243 

5.79944 

13 

48 

.10158 

9.84482 

.11924 

8.38625 

.13698 

7.30018 

.15481 

6.45961 

.17273 

5.78938 

12 

49 

.10187 

9.81641 

.119f4 

8.36555 

.13728 

7.28442 

.15511 

6.44720 

.17303 

5.77936 

11 

50 

.10216 

9.78817 

.11983 

8.34496 

.13758 

7.26873 

.15540 

6.43484 

.17333 

5.76937 

10 

51 

.10246 

9.76009 

.12013 

8,32446 

.13787 

7.25310 

.15570 

6.42253 

.17363 

5.75941 

9 

52 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

.15600 

6.41026 

.17393 

5.74949 

8 

53 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

.15630 

6.39804 

.17423 

5.73960 

7 

54 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20661 

.15660 

6.38587 

.17453 

5.72974 

55 

.10363 

9.64935 

.12131 

8.24345 

.13906 

7.19125 

.15689 

6.37374 

.17483 

5.71992 

56 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

.15719 

6.36165 

.17513 

5.71013 

57 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

.15749 

6.34961 

.17543 

5.70037 

58 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

.15779 

6.33761 

.17573 

5.69064 

59 

.10481 

9.54106 

.12249 

8.16398 

.14024 

7.13042 

.15809 

6.32566 

.17603 

5.68094 

60 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

.17633 

5.67128 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

8- 

1° 

85 

*° 

8 

2° 

«• 

L° 

8 

0° 

t 

366 


MINE  GASES  AND  VENTILATION 


1( 

IP 

1 

1° 

1 

2° 

1 

JP 

] 

40 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

60 

.17663 

5.66165 

.19468 

5.13658 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

59 

.17693 

5.65205 

.19498 

5.12862 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

58 

.17723 

5.64248 

.19529 

5.12069 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

57 

.17753 

5.63295 

.19559 

5.11279 

.21377 

4.67786 

.23209 

4.308CO 

.25056 

3.99099 

56 

.17783 

5.62344 

.19589 

5.10490 

.21408 

4.67121 

.23240 

4.30291 

.25087 

3.98607 

55 

.17813 

5.61397 

.19619 

5.09704 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

54 

.17843 

5.60452 

.19(549 

5.08921 

.21469 

4.G5797 

.23301 

4.29159 

.25149 

3.97627 

53 

.17873 

5.59511 

.19680 

5.08139 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

52 

.17903 

5.58573 

.19710 

5.07360 

.21529 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

51 

10 

.17933 

5.57638 

.19740 

5.06584 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

50 

11 

.17963 

5.56706 

.19770 

5.05809 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

49 

12 

.17993 

5.55777 

.19801 

5.05037 

.21621 

4.62518 

.23455 

4.26352 

.25304 

3.95196 

48 

13 

.18023 

5.54851 

.19831 

5.04267 

.21651 

4.61868 

.23485 

4.25795 

.25335 

3.94713 

47 

14 

.18053 

5.53927 

.19861 

5.03499 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

46 

15 

.18083 

5.53007 

.19891 

5.02734 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

45 

16 

.18113 

5.52090 

.19921 

5.01971 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

44 

17 

.18143 

5.51176 

.19952 

5.01210 

.21773 

4.59283 

.23608 

4.2C530 

.25459 

3.92793 

43 

18 

.18173 

5.50264 

.19982 

5.00451 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

42 

19 

.18203 

5.49356 

.20012 

4.99695 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

41 

20 

.18233 

5.48451 

.20042 

4.98940 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91364 

40 

21 

.182«3 

5.47548 

.20073 

4.98188 

.21895 

4.56726 

.23731 

4.21387 

.25583 

3.90890 

39 

22 

.18293 

5.46648 

.20103 

4.97438 

.21925 

4.56091 

.23762 

4.20842 

.25614 

3.90417 

38 

23 

.18323 

5.45751 

.20133 

4.96690 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

37 

24 

.18353 

5.44857 

.20164 

4.95945 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

36 

25 

.18384 

5.43966 

.20194 

4.95201 

.22017 

4.54196 

.23854 

4.19215 

.25707 

3.89004 

35 

26 

.18414 

5.43077 

.20224 

4.94460 

.22047 

4.53568 

.23885 

4.18675 

.25738 

3.88536 

34 

27 

.18444 

5.42192 

.20254 

4.93721 

.22078 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

33 

28 

.18474 

5.41309 

.20285 

4.92984 

.22108 

4.52316 

.23946 

4.17600 

.25800 

3.87601 

32 

29 

.18504 

5.40429 

.20315 

4.92249 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

31 

30 

.18534 

5.39552 

.20345 

4.91516 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

30 

31 

.18564 

5.38677 

.20376 

4.90785 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

29 

82 

.18594 

5.37805 

.20406 

4.90056 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

28 

33 

.18624 

5.36936 

.20436 

4.89330 

.22261 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

27 

34 

.18654 

5.36070 

.20466 

4.88605 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

26 

35 

.18684 

5.35206 

.20497 

4.87882 

.22322 

4.47986 

.24162 

4.13877 

.26017 

3.84364 

25 

36 

.18714 

5.34345 

.20527 

4.87162 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

24 

87 

.18745 

5.33487 

.20557 

4.86444 

.22383 

4.46764 

.24223 

4.12825 

.26079 

3.83449 

23 

38 

.18775 

5.32631 

.20588 

4.85727 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

22 

39 

.18805 

5.31778 

.20618 

4.85013 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

21 

40 

.18835 

5.30928 

.20648 

4.84300 

.22475 

4.44942 

.24316 

4.11256 

.26172 

3.82083 

20 

41 

.18865 

5.30080 

.20679 

4.83590 

.22505 

4'.44338 

.24347 

4.10736 

.26203 

3.81630 

19 

42 

.18895 

5.29235 

.20709 

4.82882 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

18 

43 

.18925 

5.28393 

.20739 

4.82175 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

17 

44 

.18955 

5.27553 

.20770 

4.81471 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80276 

16 

45 

.18986 

5.26715 

.20800 

4.80769 

.22628 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

15 

46 

.19016 

5.25880 

.20830 

4.80068 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

14 

47 

.19046 

5.25048 

.20861 

4.79370 

.22689 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

13 

48 

.19076 

5.24218 

.20891 

4.78673 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.78485 

12 

49 

.19106 

5.23391 

.20921 

4.77978 

.22750 

4.39560 

.24593 

4.06616 

.26452 

S.  78040 

11 

50 

.19136 

5.22566 

.20952 

4.77286 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

10 

51 

.19166 

5.21744 

.20982 

4.76595 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

62 

.19197 

5.20925 

.21013 

4.75906 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

63 

.19227 

5.20107 

.21043 

4.75219 

.22872 

4.37207 

.24717 

4.04586 

.26577 

3.76268 

64 

.19257 

5.19293 

.21073 

4.74534 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

55 

.19287 

5.18480 

.21104 

4.73851 

.22934 

4.36040 

.24778 

4.03578 

.26639 

3.75388 

66 

.19317 

5.17671 

.21134 

4.73170 

.22964 

4.35459 

.24809 

4.03076 

.26670 

3.74950 

67 

.19347 

5.16863 

.21164 

4.72490 

.22995 

4.34879 

.24840 

4.02574 

.26701 

3.74512 

58 

.19378 

5.16058 

.21195 

4.71813 

.23026 

4.34300 

.24871 

4.02074 

.26733 

3.74075 

68 

.19408 

5.15256 

.21225 

4.71137 

.23056 

4.33723 

.24902 

4.01576 

.26764 

3.73640 

60 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

7* 

1° 

'  71 

5° 

T, 

o 

7< 

o 

7 

5° 

/ 

TANGENTS  AND  COTANGENTS 


307 


/ 

1 

3° 

1 

5° 

1 

7° 

1* 

*° 

1 

9° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

.16795 

3.73205 

.28675 

3.48741 

.30573 

8.27085 

.32492 

3.07768 

.34438 

J.  90421 

60 

.26826 

3.72771 

.28706 

3.48359 

.30605 

8.26745 

.32524 

3.07464 

.34465 

2.90147 

69 

26857 

3.72338 

.28738 

3.47977 

.30637 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

68 

.26888 

3.71907 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

67 

.26920 

3.71476 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2.89327 

66 

.26951 

3.71046 

'  .28832 

3.46837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

65 

.26982 

3.70616 

.28864 

3.46458 

.30764 

3.25055 

.32685 

3.05950 

.34628 

2.88783 

64 

.27013 

3.70188 

.28895 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

63 

.27044 

3.69761 

.28927 

3.45703 

.30828 

8.24383 

.32749 

3.05349 

.34693 

2.88240 

62 

.27076 

3.69335 

.28958 

3.45327 

.80860 

8.24049 

.32782 

3.05049 

.34728 

2.87970 

61 

10 

.27107 

3.68909 

.28990 

3.44951 

.30891 

8.23714 

.32814 

3.04749 

.34758 

2.87700 

60 

11 

.27138 

3.68485 

.29021 

3.44576 

.80923 

8.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.27169 

3.68061 

.29053 

3.44202 

.30955 

8.23048 

.82878 

3.04152 

.34824 

2.87161 

48 

13 

.27201 

3.67638 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.27232 

3.67217 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.27263 

3.66796 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2.86356 

45 

16 

.27294 

3.66376 

.29179 

3.42713 

.81083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

.27326 

3.65957 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

18 

.27357 

3.65538 

.29242 

3.41973 

.31147 

3.21063 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.27388 

3.65121 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.27419 

3.64705 

.29305 

3.41236 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.27451 

3.64289 

.29337 

3.40869 

.31242 

3.20079 

.33169 

3.01489 

.35118 

2.84758 

39 

22 

.27482 

3.63874 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

.27513 

3.63461 

.29400 

3.40136 

.31306 

3.19426 

.33233 

3.00903 

.35183 

2.84229 

37 

24 

.27545 

3.63048 

.29432 

3.39771 

.31338 

3.19100 

.33266 

3.00611 

.35216 

2.83965 

36 

25 

.27576 

3.62636 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

26 

.27607 

3.62224 

.29495 

3.39042 

.31402 

8.18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27 

.27638 

3.61814 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

33 

28 

.27670 

3.61405 

.29558 

3.38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

32 

29 

.27701 

3.60996 

.29590 

8.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

3t 

30 

.27732 

3.60588 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98868 

.35412 

2.82391 

30 

31 

.27764 

3.60181 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.98580 

.35445 

2.82130 

29 

32 

.27795 

3.59775 

.29685 

3.36875 

.31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

83 

.27826 

3.59370 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81610 

27 

34 

.27858 

3.58966 

,29748 

3.36158 

.31658 

3.15877 

.33589 

2.97717 

.35543 

2.81350 

26 

35 

.27889 

3.58562 

.29780 

3.35800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.27921 

3.58160 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2.97144 

.35608 

2.80833 

24 

37 

.27952 

3.57758 

.29843 

8.35087 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.27983 

3.57357 

.29875 

3.34732 

.31786 

3.14605 

.33718 

2.96573 

.35674 

2.80316 

22 

39 

.28015 

3.56957 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.28046 

3.56557 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.28077 

3.56159 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.28109 

3.55761 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.70289 

18 

43 

.28140 

3.55364 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

n 

44 

.28172 

3.54968 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

16 

45 

.28203 

3.54573 

.30097 

3.32264 

.32010 

8.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.28234 

3.54179 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.28266 

3.53785 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

13 

48 

.28297 

3.53393 

.30192 

3.31216 

.32106 

8.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.28329 

3.53001 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2.77507 

11 

60 

.28360 

3.52609 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

.28391 

3.52219 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92910 

.36101 

2.77002 

52 

.28423 

3.51829 

.30319 

3.29829 

.32235 

3.10223 

.34173 

2.92632 

.36134 

2.76750 

53 

.28454 

3.51441 

.30351 

3.29483 

.32267 

3.09914 

.34205 

2.92354 

.36167 

2.76498 

54 

.28486 

3.51053 

.30382 

3.29139 

.32299 

3.09606 

.34238 

2.92076 

.36199 

2.76247 

55 

.28517 

3.50666 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.36232 

2.75996 

56 

.28549 

3.50279 

.30446 

8.28452 

.32363 

3.08991 

.34303 

2.91523 

.36265 

2.75746 

57 

.28580 

3.49894 

.30478 

3.28109 

.32386 

3.08685 

.34335 

2.91246 

.36298 

2.75496 

58 

.28612 

3.49509 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.36331 

2.75246 

59 

.28643 

3.49125 

.30541 

3.27426 

.32460 

3.08073 

.34400 

2.90696 

.36364 

2.74997 

60 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

.36397 

2.74748 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

f 

7 

1° 

7 

3° 

7 

2° 

7: 

L° 

7( 

)° 

f 

368 


MINE  GASES  AND  VENTILATION 


1 

21 

IP 

2 

L° 

2 

2° 

2 

J° 

a 

4° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

.36397 

2.74748 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

60 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

.44558 

2.24428 

59 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

.44593 

2.24252 

58 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

.44627 

2.24077 

57 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

.44662 

2.23902 

56 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.84636 

.44697 

2.23727 

55 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

.44732 

2.23553 

54 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

.44767 

2.23378 

53 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

.44802 

2.23204 

52 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

.42757 

2.33881 

.44837 

2.23030 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

.44872 

2.22857 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

.44907 

2.22683 

49 

12 

.86793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

.44942 

2.22510 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

.44977 

2.22337 

47 

H 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

.45012 

2.22164 

46 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

.45047 

2.21992 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

.45082 

2.21819 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

.45117 

2.21647 

43 

18 

.36991 

2.70335 

.38988 

2.56487 

.41013 

2.43825 

.43067 

2.32197 

.45152 

2.21475 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

,43101 

2.32012 

.45187 

2.21304 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

.45222 

2.21132 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

.45257 

2.20961 

89 

23 

.87123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

43205 

2.31456 

.45292 

2.20790 

88 

25 

.37157 

2.69131 

.39156 

2.55389 

.41183 

2.42819 

.43239 

2.31271 

.45327 

2.20619 

87 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

.45362 

2.20449 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

.45397 

2.20278 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

.45432 

2.20108 

34 

V 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

.45467 

2.19938 

33 

28 

.37322 

2.67937 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

.45502 

2.19769 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41387 

2.41G20 

.43447 

2.30167 

.45538 

2.19599 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

.45573 

2.19430 

30 

81 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

.45608 

2.19261 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

.45643 

2.19092 

28 

33 

.37488 

2.  '66752 

.39492 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

.45678 

2.18923 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

.45713 

2.18755 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

.45748 

2.18587 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

.45784 

2.18419 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

.45819 

2.18251 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

.45854 

2.18084 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

.45889 

2.17916 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

.45924 

2.17749 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

.45960 

2.17582 

19 

42 

.37787 

2.64642 

.39*95 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

.45995 

2.17416 

18 

48 

.37820 

2.64410 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2.27626 

.46030 

2.17249 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41899 

2.38668 

.43966 

2.27447 

.46065 

2.17083 

16 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

.46101 

2.16917 

15 

46 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

.46136 

2.16751 

14 

47 

.37953 

2.63483 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.26909 

.46171 

2.16585 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2.37891 

.44105 

2.26730 

.46206 

2.16420 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.42070 

2.37697 

.44140 

2.26552 

.46242 

2.16255 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

.46277 

2.16090 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

.46312 

2.15925 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

,44244 

2.26018 

.46348 

2.15760 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

.46383 

2.15596 

54 

.38186 

2.61874 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

.46418 

2.15432 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

.46454 

2.15268 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

.46489 

2.15104 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

.46525 

2.14940 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

.46560 

2.14777 

59 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

.46595 

2.14614 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

.46631 

2.14451 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

T*ng 

/ 

6< 

)° 

6* 

0 

6' 

rO 

6f 

o 

6, 

)° 

TANGENTS  AND  COTANGENTS 


369 


2i 

)° 

2t 

0 

X 

o 

2£ 

o 

2 

J° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang. 

Tang 

Cotang 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80405 

60 

.46666 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

.53208 

1.87941 

.55469 

1.80281 

59 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

.53246 

1.87809 

.65507 

1.80158 

68 

.46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

.53283 

1.87677 

.55545 

1.80034 

57 

.46772 

2.13801 

.48917 

2.04426 

.51099 

1.95698 

.53320 

1.87546 

.55583 

1.79911 

56 

.46808 

2.13639 

.48953 

2.04276 

.51136 

1.95557 

.53358 

1.87415 

.55621 

1.79788 

55 

.46843 

2.13477 

.48989 

2.04125 

.51173 

1.95417 

.53395 

1.87283 

.65659 

1.79665 

54 

.46879 

2.13316 

.49026 

2.03975 

.51209 

1.95277 

.53432 

1.87152 

.55697 

1.79542 

53 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

.53470 

1.87021 

.55736 

1.79419 

52 

.46950 

2.12993 

.49098 

2.03675 

.51283 

1  .94997 

.53507 

1.86891 

.55774 

1.79296 

51 

10 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

.53545 

1.86760 

.55812 

1.79174 

60 

11 

.47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

.63582 

1.86630 

.55850 

1.79051 

49 

12 

.47056 

2.12511 

.49206 

2.03227 

.51393 

1.94579 

.53620 

1.86499 

.55888 

1.78929 

48 

13 

.47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

.53657 

1.86369 

.55926 

1.78807 

47 

14 

.47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

.53694 

1.86239 

.55964 

1.78685 

46 

15 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

.53732 

1.86109 

.56003 

1.78563 

45 

16 

.47199 

2.11871 

.49351 

2.02631 

.51540 

1.94023 

.53769 

1.85979 

.56041 

1.78441 

44 

17 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

.53807 

1.85850 

.56079 

1.78319 

43 

18 

.47270 

2.11552 

.49423 

2.02335 

.51614 

1.93746 

.53844 

1.85720 

.56117 

1.78198 

42 

19 

.47305 

2.11392 

.49459 

2.02187 

.51651 

1.93608 

.53882 

1.85591 

.56156 

1.78077 

41 

20 

.47341 

2.11233 

.49495 

2.02039 

.51688 

1.93470 

.53920 

1.85462 

.56194 

1.77955 

40 

21 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

.53957 

1.85333 

.56232 

1.77834 

39 

22 

.47412 

2.10916 

.49568 

2.01743 

.51761 

1.93195 

.53995 

1.85204 

.56270 

1.77713 

38 

23 

.47448 

2.10758 

.49604 

2.01596 

.51798 

1.93057 

.54032 

1.85075 

.56309 

1.77592 

37 

24 

.47483 

2.10600 

.49640 

2.01449 

.51835 

1.92920 

.54070 

1.84946 

.56347 

1.77471 

36 

25 

.47519 

2.10442 

.49677 

2.01302 

.51872 

1.92782 

.54107 

1.84818 

.56385 

1.77351 

35 

26 

.47555 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

.54145 

1.84689 

.56424 

1.77230 

34 

27 

.47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

.54183 

1.84561 

.56462 

1.77110 

33 

28 

.47626 

2.09969 

.49786 

2.00862 

.51983 

1.92371 

.54220' 

1.84433 

.56501 

1.76990 

32 

29 

.47662 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

.54258 

1.84305 

.56539 

1.76869 

31 

30 

.47698 

2.09654 

.49858 

2.00569 

.52057 

1.92098 

.54296 

1.84177 

.56577 

1.76749 

30 

31 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

.54333 

1.84049 

.56616 

1.76629 

29 

32 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

.54071 

1.83922 

.56654 

1.76510 

28 

33 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91C90 

.54409 

1.83794 

.56693 

1.76390 

27 

34 

.47840 

2.09028 

.50004 

1.99986 

.52205 

1.91554 

.54446 

1.83667 

.56731 

1.76271 

26 

35 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91418 

.54484 

1.83540 

.56769 

1.76151 

25 

36 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91282 

.54522 

1.83413 

.56808 

1.76032 

24 

37 

.47948 

2.08560 

.50113 

1.99550 

.52316 

1.91147 

.54560 

1.83286 

.56846 

1.75913 

23 

38 

.47984 

2.08405 

.50149 

1.99406 

.52353 

1.91012 

.54597 

1.83159 

.56885 

1.75794 

22 

39 

.48019 

2.08250 

.50185 

1.99261 

.52390 

1.90876 

.54635 

1.83033 

.56923 

1.75675 

21 

40 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

.54673 

1.82906 

.56962 

1.75556 

20 

41 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

.54711 

1.82780 

.57000 

1.75437 

19 

42 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

.54748 

1.82654 

.57039 

1.75319 

18 

43 

.48163 

2.  7630 

.50331 

1.98684 

.52538 

1.90337 

.54786 

1.82528 

.57078 

1.75200 

17 

44 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

.54824 

1.82402 

.57116 

1.75082 

16 

45 

.48234 

2  07321 

.50404 

1.98396 

.52613 

1.90069 

.54862 

1.82276 

.57155 

1.74964 

15 

46 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

.54900 

1.82150 

.57193 

1.74846 

14 

47 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

.54938 

1.82025 

.57232 

1.74728 

13 

48 

.48342 

2.06860 

.50514 

1.97966 

.52724 

1.89667 

.54975 

1.81899 

.57271 

1.74610 

12 

49 

.48378 

2.06706 

.50550 

1.97823 

.52761 

1.89533 

.55013 

1.81774 

.57309 

1.74492 

11 

50 

.48414 

2.06553 

.50587 

1.97681 

.52798 

1.89400 

.55051 

1.81649 

.57348 

1.74375 

10 

61 

.48450 

2.06400 

.50623 

1.97538 

.52836 

1.89266 

.55089 

1.81524 

.57386 

1.74257 

52 

.48486 

2.06247 

.50660 

1.97395 

.52873 

1.89133 

.55127 

1.81399 

.57425 

1.74140 

63 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

.55165 

1.81274 

.57464 

1.74022 

64 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

.55203 

1.81150 

.57503 

1.73905 

55 

.48593  ' 

2.05790 

.50769 

1.96969 

.52985 

1.88734 

.55241 

1.81025 

.57541 

1.73788 

56 

.48629 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

.55279 

1.80901 

.57580 

1.73671 

57 

.48665 

2.05485 

.50843 

1.96685 

.53059 

1.88469 

.55317 

1.80777 

.57619 

1.73565 

58 

.48701 

2.05333 

.50879 

1.96544 

.53096 

1.88337 

.55355 

1.80653 

.57657 

1.73438 

59 

.48737 

2.05182 

.50916 

1.96402 

.53134 

1.88205 

.55393 

1.80529 

.5769ft 

1.73321 

60 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80406 

.57735 

1.73205 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

fr 

1° 

6, 

J° 

e: 

>o 

C] 

0 

8 

y> 

t 

370 


MINE  GASES  AND  VENTILATION 


f 

3( 

)° 

3] 

0 

31 

to 

Si 

5° 

& 

1° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.57735 

1.73205 

.60086 

1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

60 

.57774 

1.73089 

.60126 

1.66318 

.62527 

1.59930 

.64982 

1.53888 

.67493 

1.48163 

59 

2 

.57813 

1.72973 

.60165 

1.66209 

.62568 

1.59826 

.65024 

1.53791 

.67536 

1.48070 

58 

3 

.57851 

1.72857 

.60205 

1.66099 

.62608 

1.59723 

.65065 

1.53693 

.67578 

1.47977 

57 

4 

.57890 

1.72741 

.60245 

1.65990 

.62649 

1.59620 

.65106 

1.53595 

.67620 

1.47885 

56 

5 

.57929 

1.72625 

.60284 

1.65881 

.62689 

1.59517 

.65148 

1.53497 

.67663 

1.47792 

55 

6 

.57968 

1.72509 

.60324 

1.65772 

.62730 

1.59414 

.65189 

1.53400 

.67705 

1.47699 

54 

7 

.58007 

1.72393 

.60364 

1.65663 

.62770 

1.59311 

.65231 

1.53302 

.67748 

1.47607 

53 

8 

.58046 

1.72278 

.60403 

1.65554 

.62811 

1.59208 

.65272 

1.53205 

.67790 

1.47514 

52 

9 

.58085 

1.72163 

.60443 

1.65445 

.62852 

1.59105 

.65314 

1.53107 

.67832 

1.47422 

51 

10 

.58124 

1.72047 

.60483 

1.65337 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.47330 

50 

11 

.58162 

1.71932 

.60522 

1.65228 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

49 

12 

.58201 

1.71817 

.60562 

1.65120 

.62973 

1.58797 

.65438 

1.52816 

.67960 

1.47146 

48 

13 

.58240 

1.71702 

.60602 

1.65011 

.63014 

1.58695 

.65480 

1.52719 

.68002 

1.47053 

47 

14 

.58279 

1.71588 

.60642 

1.64903 

.63055 

1.58593 

.65521 

1.52622 

.68045 

1.46962 

46 

IS 

.58318 

1.71473 

.60681 

1.64795 

.63095 

1.58490 

.65563 

1.52525 

.68088 

1.46870 

45 

16 

.58357 

1.71358 

.60721 

1.64687 

.63136 

1.58388 

.65604 

1.52429 

.68130 

1.46778 

44 

17 

.58396 

1.71244 

.60761 

1.64579 

.63177 

1.58286 

.65646 

1.52332 

.68173 

1  .46686 

43 

18 

.58435 

1.71129 

.60801 

1.64471 

.63217 

1.58184 

.65688 

1.52235 

.68215 

1.46595 

42 

19 

.58474 

1.710,15 

.60841 

1.64363 

.63258 

1.58083 

.65729 

1.52139 

.68258 

1.46503 

41 

20 

.58513 

1.70901 

.60881 

1.64256 

.63299 

1.57981 

.65771 

1.52043 

.68301 

1.46411 

40 

21 

.58552 

1.70787 

.60921 

1.64148 

.63340 

1.57879 

.65813 

1.51946 

.68343 

1.46320 

39 

22 

.58591 

1.70673 

.60960 

1.64041 

.63380 

1.57778 

.65854 

1.51850 

.68386 

1.46229 

38 

23 

.58631 

1.70560 

.61000 

1.63934 

.63421 

1.57676 

.65896 

1.51754 

.68429 

1.46137 

37 

24 

.58670 

1.70446 

.61040 

1.63826 

.63462 

1.57575 

.65938 

1.51658 

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.91580 

1.09195 

.94841 

1.05439 

.98213 

1.01820 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

.98270 

1.01761 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.0531? 

.98327 

1.01702 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

.98384 

1.01642 

28 

33 

.85559 

1.16878 

.88628 

1.12831 

.91794 

1.08940 

.95062 

1.05194 

.98441 

1.01583 

27 

34 

.85609 

1.16809 

.88680 

1.12765 

.91847 

1.08876 

.95118 

1.05133 

.98499 

1.01524 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.91901 

1.08813 

.95173 

1.05072 

.98556 

1.01465 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

.98613 

1.01406 

24 

37 

.85761 

1.16603 

.88836 

1.12567 

.92008 

1.08686 

.95284 

1.04949 

.98671 

1.01347 

23 

38 

.85811 

1.16535 

1.12501 

.92062 

1.08622 

.95340 

1.04888 

.98728 

1.01288 

22 

39 

.85862 

1.16466 

!88940 

1.12435 

.92116 

1.08559 

.95395 

1.04827 

.98786 

1.01229 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08496 

.95451 

1.04766 

.98843 

1.01170 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

.98901 

1.01112 

19 

42 

.86014 

1.16261 

.89097 

.12238 

.92277 

1.08369 

.95562 

1.04644 

.98958 

1.01053 

18 

43 

.86064 

1.16192 

.89149 

.12172 

.92331 

1.08306 

.95618 

1.04583 

.99016 

1.00994 

17 

44 

.86115 

1.16124 

.89201 

.12106 

.92385 

1.08243 

.95673 

1.04522 

.9C073 

1.00935 

16 

45 

.86166 

1.16056 

.89253 

.12041 

.92439 

1.08179 

.95729 

1.04461 

.901  31 

1.00876 

15 

46 

.8621  6 

1.15987 

.11975 

.924'J3 

1.08116 

.95785 

1.04401 

.99189 

1.00818 

14 

47 

.86267 

1.15919 

!89358 

.11909 

.92547 

1.08053 

.95841 

1.04340 

.99247 

1  .00759 

13 

48 

.86318 

1.15851 

.89410 

.11844 

.92601 

1.07990 

.95897 

1.04279 

.99304 

1.00701 

12 

49 

.86368 

1.15783 

.89463 

.11778 

.92655 

1.07927 

.95952 

1.04218 

.99362 

1.00642 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

.99420 

1.00583 

10 

51 

.86470 

1.15647 

.89567 

.11648 

.92763 

1.07801 

.96064 

1.04097 

.99478 

1.00525 

C2 

.86521 

1.15579 

.89620 

1.11532 

.92817 

1.07738 

.96120 

1.04036 

.99536 

1.00467 

53 

-86572 

1.15511 

.89672 

1.11517 

.92872 

1.07676 

.96176 

1.03976 

.99594 

1.00408 

54 

-86623 

1.15413 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

.!i9f>52 

1.00350 

55 

86674 

1.15375 

.89777 

.92980 

1.07550 

.96288 

1.03855 

.99710 

1  .00291 

56 

86725 

1.15308 

.89830 

l!l!321 

.93034 

1.07487 

.96344 

1.03794 

.99768 

1.00233 

57 

.86776 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

.99826 

1.00175 

58 

.86827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.96457 

1.03674 

.99884 

1.00116 

59 

.86878 

1.15104 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

.99942 

1.00058 

60 

.86929 

1.15037 

190040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

1.00000 

1.00000 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

7 

4 

J° 

45 

S° 

4 

1° 

4( 

)° 

4 

5° 

SQUARES,  CUBES,  ROOTS  AND  RECIPROCALS 

OF  NUMBERS,  CIRCUMFERENCES  AND 

AREAS  OF  CIRCLES 


373 


374 


MINE  GASES  AND  VENTILATION 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 
CIRCUMFERENCES,  AND  AREAS 


No. 

Squure 

Cube 

Sq.  Root 

Cu.Root 

Eeciprocdl 

Circum. 

Area 

1 

1 

1 

1.0000 

1.0000 

1.000000000 

3.1416 

0.7854 

2 

4 

8 

1.4142 

1.2599 

.500000000 

6.2832 

3.1416 

3 

9 

27 

1.7321 

1.4422 

.333333333 

9.4248 

7.0686 

4 

16 

64 

2.0000 

1.5874 

.250000000 

12.5GG1 

12.5664 

5 

25 

125 

2.2361 

1.7100 

.200000000 

15.7080 

19.635 

6 

36 

216 

2.4495 

1.8171 

.1G6666G67 

18.850 

28.274 

7 

49 

343 

2.6458 

1.9129 

.1-12857143 

21.991 

38.485 

8 

64 

512 

2.8284 

2.0000 

.125000000 

25.133 

50.266 

9 

81 

729 

3.0000 

2.0801 

.111111111 

28.274 

63.617 

10 

100 

1,000 

3.1623 

2.1544 

.100000000 

31.416 

78.540 

11 

121 

1,331 

3.3166 

2.2240 

.090909091 

34.558 

95.033 

12 

144 

1,728 

3.4641 

2.2894 

.083333333 

37.699 

113.10 

13 

169 

2,197 

3.6056 

2.3513 

.076923077 

40.841 

132.73 

14 

196 

2,744 

3.7417 

2.4101 

.071428571 

43.982 

153.94 

15 

225 

3,375 

3.8730 

2.4662 

.066666667 

47.124 

176.71 

16 

256 

4,096 

4.0000 

2.5198 

.062500000 

50.265 

201.06 

17 

289 

4,913 

4.1231 

2.5713 

.058823529 

53.407 

226.98 

18 

324 

5,832 

4.2426 

2.6207 

.055555556 

56.549 

254.47 

19 

361 

6,859 

4.3589 

2.C684 

.052631579 

59.690 

283.53 

20 

400 

8,000 

4.4721 

2.7144 

.050000000 

62.832 

314.16 

21 

441 

9,261 

4.5826 

2.7589 

.047619048 

65.973 

346.36 

22 

484 

10,648 

4.6904 

2.8020 

.045454545 

69.115 

380.13 

23 

529 

12,167 

4.7958 

2.8439 

.043478261 

72.257 

415.48 

24 

"  576 

13,824 

4.8990 

2.8845 

.041666667 

75.398 

452.39 

25 

625 

15,625 

5.0000 

2.9240 

.040000000 

78.540 

490.87 

26 

676 

17,576 

5.0990 

2.9625 

.038461538 

81.C81 

530.93 

27 

729 

19,683 

5.1962 

3.0000 

.037037037 

84.823 

572.56 

28 

784 

21,952 

5.2915 

3.0366 

.035714286 

87.965 

615.75 

29 

841 

24,389 

5.3852 

3.0723 

.034482759 

91.106 

660.52 

30 

900 

27,000 

5.4772 

3.1072 

.033333333 

94.248 

706.86 

31 

961 

29,791 

5.5678 

3.1414 

.0322,58065 

97.389 

754.77 

32 

1,024 

32,768 

5.65G9 

3.1748 

.031250000 

100.53 

804.25 

33 

1,089 

35,937 

5.7446 

3.2075 

.030303030 

103.67 

855.30 

34 

1,156 

39,304 

5.8310 

3.2396 

.029411765 

106.81 

907.92 

35 

1,225 

42,875 

5.9161 

3.2717 

.028571429 

109.96 

962.11 

36 

1,296 

46,656 

•  6.0000 

3.3019 

.027777778 

113.10 

1,017.88 

37 

1,369 

50,653 

6.0828 

3.3322 

.027027027 

116.24 

1,075.21 

38 

1,444 

54,872 

6.1644 

3.3620 

.026315789 

119.38 

1,134.11 

39 

1,521 

59,319 

6.2450 

3.3912 

.025641026 

122.52 

1,194.59 

40 

1,600 

64,000 

6.3246 

3.4200 

.025000000 

125.66 

1,256.64 

41 

1,681 

68,921 

6.4031 

3.4482 

.024390244 

128.81 

1,320.25 

42 

1,764 

74,088 

6.4807 

3.4760 

.023809524 

131.95 

1,385.44 

43 

1,849 

79,507 

6.5574 

35034 

.023255814 

135.09 

1,452.20 

44 

1,936 

85,184 

6.6332 

3  5303 

.022727273 

138.23 

1,520.53 

45 

2,025 

91,125 

6.7082 

3.55G9 

.022222222 

141.37 

1,590.43 

46 

2,116 

97,336 

67823 

35830 

.021739130 

144.51 

1,061.90 

47 

2,209 

103,823 

68557 

36088 

.021276600 

147.65 

1,734.94 

48 

2,304 

110,592 

6.9282 

3.6342 

.020833333 

150.80 

1,809.56 

49 

2,401 

117,6-19 

7.0000 

36593 

.020408163 

153.94 

1,885.74 

50 

2,500 

125,000 

7.0711 

3.6S40 

.020000000 

157.08 

1,963.50 

51 

2,601 

132,651 

7.1414 

3.7084 

.019607843 

160.22 

2,042.82 

52 

2,704 

140,608 

7.2111 

3.7325 

.019230769 

63.36 

2.123.72 

53 

2,809 

148,877 

7.2801 

3.7563 

.018867925 

66.50 

2,206.18 

54 

2,916 

157,464 

7.3485 

3.7798 

.018518519 

69.65 

2,290.22 

65 

3,025 

166,375 

7.4162 

3.8030 

.018181818 

72.79 

2,375.83 

SQUARES,  CTrBES,  ROOTS,  ETC. 


375 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Boot 

Reciprocal 

Circum 

Area 

56 

3,136 

175,616 

7.4833 

3.8259 

.017857143 

175.93 

2,463.01 

57 

3,249 

185,193 

7.5498 

3.8485 

.017543860 

179.07 

2,551.76 

58 

3,364 

195,112 

7.6158 

3.8709 

.017241379 

182.21 

2,642.08 

59 

3,481 

205,379 

7.6811 

3.8930 

.016949153 

185.35 

2,733.97 

60 

3,600 

216,000 

7.7460 

3.9149 

.016666667 

188.50 

2,827.43 

61 

8,721 

226,981 

7.8102 

3.9365 

.016393443 

191.64 

2,922.47 

62 

3,844 

238,328 

7.8740 

3.9579 

.016129032 

194.78 

3,019.07 

63 

8,969 

250,047 

7.9373 

3.9791 

.015873016 

197.92 

3,117.25 

64 

4,096 

262,144 

8.0000 

4.0000 

.015625000 

201.06 

3,216.99 

65 

4,225 

274,625 

8.0623 

4.0207 

.015384615 

204.20 

8,318.31 

66 

4,356 

287,496 

8.1240 

4.0412 

.015151515 

207.34 

3,421.19 

67 

4,489 

300,763 

8.1854 

4.0615 

.014925373 

210.49 

3,525.65 

68 

4,624 

314,432 

8.2462 

4.0817 

.014705882 

213.63 

3,631.68 

69 

4,761 

328,509 

8.3066 

4.1016 

.014492754 

216.77 

3,739.28 

70 

4,900 

343,000 

8.36G6 

4.1213 

.014285714 

219.91 

3,848.45 

71 

5,041 

357,911 

8.4261 

4.1408 

.014084517 

223.05 

3,959.19 

72 

5,184 

373,248 

8.4853 

4.1602 

.013888889 

226.19 

4,071.50 

73 

5,329 

389,017 

8.5440 

4.1793 

.013698630 

229.34 

4,185.39 

74 

6,476 

405,224 

8.6023 

4.1983 

.013513514 

232.48 

4,300.84 

75 

5,625 

421,875 

8.6603 

4.2172 

.013333333 

235.62 

4,417.86 

76 

5,776 

438,976 

8.7178 

4.2358 

.013157895 

238.76 

4,536.46 

77 

5,929 

456,533 

8.7750 

4.2543 

.012987013 

241.90 

4,656.63 

78 

6,084 

474,552 

8.8318 

4.2727 

.012820513 

245.04 

4,778.36 

79 

6,241 

493,039 

8.8882 

4.2908 

.012658228 

248.19 

4,901.67 

80 

6,400 

512,000 

8.9413 

4.3089 

.012500000 

251.33 

5,026.55 

81 

6,561 

531,441 

9.0000 

4.3267 

.012345679 

254.47 

5,153.00 

82 

6,724 

551,368 

9.0554 

4.3445 

.012195122 

257.61 

5,281.02 

83 

6,889 

571,787 

9.1104 

4.3621 

.012048193 

260.75 

5,410.61 

84 

7,056 

592,704 

9.1652 

4.3795 

.011904762 

263.89 

5,541.77 

85 

7,225 

614,125 

9.2195 

4.3968 

.011764706 

267.04 

5,674.50 

86 

7,396 

636,056 

9.2736 

4.4140 

.011627907 

270.18 

5,808.80 

87 

7,569 

658,503 

9.3274 

4.4310 

.011494253 

273.32 

5,944.68 

88 

7,744 

681,472 

9.3808 

4.4480 

.011363G36 

276.46 

6,082.12 

89 

7,921 

704,969 

9.4340 

4.4647 

.011235955 

279.60 

6,221.14 

90 

8,100 

729,000 

9.4868 

4.4814 

.011111111 

282.74 

6,361.73 

91 

8,281 

753,571 

9.5394 

4.4979 

.010989011 

285.88 

6,503.88 

92 

8,464 

778,688 

9.5917 

4.5144 

.010869565 

289.03 

6,647.61 

93 

8,649 

804,357 

9.6437 

4.5307 

.010752688 

292.17 

6,792.91 

94 

8,836 

830,584 

9.6954 

4.5468 

.010638298 

295.31 

6,939.78 

95 

9,025 

857,375 

9.7468 

4.5629 

.010526316 

298.45 

7,088.22 

96 

9,216 

884,736 

9.7980 

4.5789 

.010416667 

301.59 

7,238.23 

97 

9,409 

912,673 

9.8489 

4.5947 

.010309278 

304.73 

7,389.81 

98 

9,604 

941,192 

9.8995 

4.6104 

.010204082 

307.88 

7,542.96 

99 

9,801 

970,299 

9.9499 

4.6261 

.010101010 

311.02 

7,697.69 

100 

10,000 

1,000,000 

10.0000 

4.6416 

.010000000 

314.16 

7,853.98 

101 

10,201 

1,030,301 

10.0499 

4.6570 

.009900990 

317.30 

8,011.85 

102 

10,404 

1,061,208 

10.0995 

4.6723 

.009803922 

320.44 

8,171.28 

103 

10,609 

1,092,727 

10.1489 

4.6875 

.009708738 

323.58 

8,332.29 

104 

10,816 

1,124,864 

10.1980 

4.7027 

.009615385 

326.73 

8,494.87 

105 

11,025 

1,157,625 

10.2470 

4.7177 

.009523810 

329.87 

8,659.01 

106 

11,236 

1,191,016 

10.2956 

4.7326 

.009433962 

333.01 

8,824.73 

107 

11,449 

1,225,043 

10.3441 

4.7475 

.009345794- 

336.15 

8,992.02 

108 

11,664 

1,259,712 

10.3923 

4.7622 

.009259259 

339.29 

9,160.88 

109 

11,881 

1,295,029 

10.4403 

4.7769 

.009174312 

342.43 

9,331.32 

110 

12,100 

1,331,000 

10.4881 

4.7914 

.009090909 

345.58 

9,503.32 

111 

12,321 

1,367,631 

10.5357 

4.8059 

.009009009 

348.72 

9,676.89 

112 

12,544 

1,404,928 

10.5830 

4.8203 

.008928571 

351.86 

9,852.03 

113 

12,769 

1,442,897 

10.6301 

4.8346 

.008849558 

355.00 

10,028.75 

114 

12,996 

1,481,544 

10.6771 

4.8-188 

.008771930 

358.14 

10,207.03 

115 

13,225 

1,520,875 

10.7238 

4.8629 

.008695652 

361.28 

10,386.89 

116 

13,456 

1,560,896 

10.7703 

4.8770 

.008020690 

364.42 

10,568.32 

117 

13,689 

1,601,613 

10.8167 

4.8910 

,00arv47009 

367.57 

10,751.32 

118 

13,924 

1,643,032 

10.8628 

4.9049 

.008474576 

370.71 

10,935.88 

376 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Hoot 

Cu.  Root 

Reciprocal 

Circum. 

AIM 

119 

14,161 

1,685,159 

10.9087 

4.9187 

.008403361 

373.85 

11,122.02 

120 

14,400 

1,728,000 

10.9545 

4.9324 

.008333333 

376.99 

11,309.73 

121 

14,641 

1,771,561 

11.0000 

4.9461 

.008264463 

380.13 

11,499.01 

122 

14,834 

1,815,848 

11.0454 

4.9597 

.008196721 

383.27 

11,689.87 

123 

15,129 

1,860,867 

11.0905 

4.9732 

.008130081 

386.42 

11,882.29 

124 

15,376 

1,906,624 

11.1355 

4.9866 

.008064516 

389.56 

12,076.28 

125 

15,625 

1,953,125 

11.1803 

5.0000 

.008000000 

392.70 

12,271.85 

126 

15,876 

2,000,376 

11.2250 

5.0133 

.007936508 

395.84 

12,468.98 

127 

16,129 

2,048,383 

11.2694 

5.0265 

.007874016 

398.98 

12,667.69 

128 

16,384 

2,097,152 

11.3137 

5.0397 

.007812500 

402.12 

12,867.96 

129 

16,641 

2,146,689 

11.3578 

5.0528 

.007751938 

405.27 

13,069.81 

130 

16,900 

2,197,000 

11.4018 

5.0658 

.007692308 

408.41 

13,273.23 

131 

17,161 

2,248,091 

11.4455 

5.0788 

.007633588 

411.55 

13,478.22 

132 

17,424 

2,299,968 

11.4891 

5.0916 

.007575758 

414.69 

13,684.78 

133 

17,689 

2,352,637 

11.5326 

5.1045 

.007518797 

417.83 

13,892.91 

134 

17,956 

2,406,104 

11.5758 

5.1172 

.007402687 

420.97 

14,102.61 

135 

18,225 

2,460,375 

11.6190 

5.1299 

.007407407 

424.12 

14,313.88 

136 

18,496 

2,515,456 

11.6619 

5.1426 

.007352941 

427.26 

14,526.72 

137 

18,769 

2,571,353 

11.7047 

5.1551 

.007299270 

430.40 

14,741.14 

138 

19,044 

2,628,072 

11.7473 

5.1676 

.00724G377 

433.54 

14,957.12 

139 

19,321 

2,685,619 

11.7898 

5.1801 

.007194245 

436.68 

15,174.68 

140 

19,600 

2,744,000 

11.8322 

5.1925 

.007142857 

439.82 

15,393.80 

111 

19,881 

2,803,221 

11.8743 

5.2048 

.007092199 

442.96 

15,614.50 

112 

20,164 

2,863,288 

11.9164 

5.2171 

.007042254 

446.11 

15,836.77 

113 

20,449 

2,924,207 

11.9583 

5.2293 

.006993007 

449.25 

16,060.61 

114 

20,736 

2,985,984 

12.0000 

5.2415 

.006944444 

452.39 

16,286.02 

115 

21,025 

3,048,625 

12.0416 

5.2536 

.006896552 

455.53 

16,513.00 

146 

21,316 

3,112,136 

12.0830 

5.2656 

.006849315 

458.67 

16,741.55 

147 

21,609 

3,176,523 

12.1244 

5.2776 

.006802721 

461.81 

16,971.67 

148 

21,904 

3,241,792 

12.1655 

5.2896 

.006756757 

464.96 

17,203.36 

149 

22,201 

3,307,949 

12.2066 

5.3015 

.006711409 

468.10 

17,436.62 

150 

22,500 

3,375,000 

12.2474 

5.3133 

.006666667 

471.24 

17,671.46 

151 

22,801 

3,442,951 

12.2882 

5.3251 

.006622517 

474.38 

17,907.86 

152 

23,104 

3,511,008 

12.3288 

5.3368 

.006578947 

477.52 

18,145.84 

153 

23,409 

3,581,577 

12.3693 

5.3485 

.00653.5948 

480.66 

18,385.39 

1.54 

23,716 

3,652,264 

12.4097 

5.3601 

.006493506 

483.81 

18,626.50 

155 

24,025 

3,723,875 

12.4499 

5.3717 

.006451613 

486.95 

18,869.19 

156 

24,336 

3,796,416 

12.4900 

5.3832 

.006410256 

490.09 

19.113.45 

157 

24,649 

3,869,893 

12.5300 

5.3947 

.006369427 

493.23 

19,359.28 

158 

24,964 

3,944,312 

12.5698 

5.4061 

.006329114 

496.37 

19,606.68 

159 

25,281 

4,019,679 

12.6095 

5.4175 

.006289308 

499.51 

19,855.65 

160 

25,600 

4,096,000 

12.6491 

5.4288 

.006250000 

502.65 

20,106.19 

161 

25,921 

4,173,281 

12.6886 

5.4401 

.006211180 

505.80 

20,358.31 

162 

26,244 

4,251,528 

12.7279 

5.4514 

.006172840 

508.94 

20,611.99 

1G3 

26,569 

4,330,747 

12.7671 

5.4626 

.006134969 

512.08 

20,867.24 

164 

26,896 

4,410,944 

12.8062 

5.4737 

.006097561 

515.22 

21,124.07 

165 

27,225 

4,492,125 

12.8452 

5.4848 

.006060606 

518.36 

21,382.46 

166 

27,556 

4,574,296 

12.8841 

5.4959 

.006024096 

521.50 

21,642.43 

167 

27,889 

4,657,463 

12.9228 

5.5069 

.005988024 

524.65 

21,903.97 

168 

28,224 

4,741,632 

12.9615 

5.5178 

.005952381 

527.79 

22,167.08 

169 

28,561 

4,826,809 

13.0000 

5.5288 

.005917160 

530.93 

22,431.76 

170 

28,900 

4,913,000 

13.9384 

5.5397 

.005882353 

534.07 

22,698.01 

171 

29,241 

5,000,211 

13.0767 

5.5505 

.005847953 

537.21 

22,965.83 

172 

29,584 

5,088,448 

13.1149 

5.5613 

.005813953 

540.35 

23,235.22 

173 

29,929 

5,177,717 

13.1529 

5.5721 

.005780347 

543.50 

23,506.18 

174 

30,276 

5,268,024 

13.1909 

5.5828 

.005747126 

546.64 

23,778.71 

175 

30,625 

5,359,375 

13.2288 

5.5934 

.005714286 

549.78 

24,052.82 

176 

30,976 

5,451,776 

13.2665 

5.6041 

.005681818 

552.92 

24,?28.49 

177 

31,329 

5,545,233 

13.3041 

5.6147 

.005649718 

556.06 

24,605.74 

178 

31,684 

5,639,752 

13.3417 

5.6252 

.005617978 

559.20 

24,884.56 

179 

32,041 

5,735,339 

13.3791 

5.6357 

.005586592 

562.35 

25,164.94 

180 

32,400 

5,832,000 

13.4164 

5.6462 

.005555556 

565.49 

25,446.90 

181 

32,761 

5,929,741 

13.4536 

5.6567 

.005524862 

568.63 

25,730.43 

SQUARES,  CUBES,  ROOTS,  ETC 


377 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Ciroum* 

Area 

182 

33,124 

6,028,568 

13.4907 

5.6671 

.005494505 

571.77 

26,015.53 

183 

33,489 

6,128,487 

13.5277 

5.6774 

.005464481 

574.91 

26,302.20 

184 

33,856 

6,229,504 

13.5647 

5.6877 

.005434783 

578.05 

26,590.44 

185 

84,225 

6,331,625 

13.6015 

5.6980 

.005405405 

581.19 

26,880.25 

186 

34,596 

6,434,856 

13.6382 

5.7083 

.005376344 

684.34 

27,171.63 

187 

34,969 

6,539,203 

13.6748 

5.7185 

.005347594 

587.48 

27,464.59 

188 

35,344 

6,644,672 

13.7113 

5.7287 

.005319149 

590.62 

27,759.11 

189 

35,721 

6,751,269 

13.7477 

5.7388 

.005291005 

593.76 

28,055.21 

190 

36,100 

6,859,000 

13.7840 

5.7489 

.005263158 

596.90 

28,352.87 

191 

36,481 

£,967,871 

13.8203 

5.7590 

.005235602 

600.04 

28,652.11 

192 

36,864 

7,077,888 

13.85G4 

5.7G90 

.005208333 

603.19 

28,952.92 

193 

37,249 

7,189,017 

13.8924 

5.7790 

.005181347 

606.33 

29,255.30 

194 

37,636 

7,301,384 

13.9284 

5.7890 

.005154639 

609.47 

29,559.25 

195 

38,025 

7,414,875 

13.9642 

5.7989 

.005128205 

612.61 

29,864.77 

196 

38,416 

7,529,536 

14.0000 

5.8088 

.005102041 

615.75 

30,171.86 

197 

38,809 

7,645,373 

14.0357 

5.8186 

.005076142 

618.89 

30,480.52 

198 

.  39,204 

7,762,392 

11.0712 

5.i>285 

.005050505 

622.04 

30,790.75 

199 

39,601 

7,880,599 

14.1067 

5.8383 

.005025126 

625.18 

31,102.55 

200 

40,000 

8,000,000 

14.1421 

5.8480 

.005000000 

628.32 

31,415.93 

201 

40,401 

8,120,601 

14.1774 

5.8578 

.004975124 

631.46 

31,730.87 

202 

40,804 

8,242,408 

14.2127 

5.8675 

.004950495 

634.60 

32,047.39 

203 

41,209 

8,365,427 

14.2478 

5.8771 

.004926108 

637.74 

32,365.47 

204 

41,616 

8,489,664 

14.2829 

5.8868 

.004901961 

640.88 

32,685.13 

205 

42,025 

8,615,125 

14.3178 

5.8964 

.004878049 

644.03 

33,006.36 

206 

42,436 

8,741,816 

14.3527 

5.9059 

.004854369 

647.17 

33,329.16 

207 

42,849 

8,869,743 

14.3875 

5.9155 

.004830918 

650.31 

33,653.53 

208 

43,264 

8,998,912 

14.4222 

5.9250 

.004807692 

653.45 

33,979.47 

209 

43,681 

9,129,329 

14.4568 

5.9345 

.004784689 

656.59 

34,306.98 

210 

44,100 

9,261,000 

14.4914 

5.9439 

.004761905 

659.73 

34,636.06 

211 

44,521 

9,393,931 

14.5258 

5.9533 

.004739336 

662.88 

34,966.71 

212 

44,944 

9,528.128 

14.5602 

5.9627 

.004716981 

666.02 

35,298.94 

213 

45,369 

9,663,597 

14.5945 

5.9721 

.004694836 

669.16 

35,632.73 

214 

45,796 

9,800,344 

14.6287 

5.9814 

.004672897 

672.30 

35,968.09 

215 

46,225 

9,938,375 

14.6629 

5.9907 

.004651163 

675.44 

36,305.03 

216 

46,656 

10,077,696 

14.6969 

6.0000 

.004629630 

678.58 

36,643.54 

217 

47,089 

10,218,313 

14.7309 

6.0092 

.004608295 

681.73 

36,983.61 

218 

47,524 

10,360,232 

14.7648 

6.0185 

.004587156 

684.87 

37,325.26 

219 

47,961 

10,503,459 

14.7986 

C.0277 

.004566210 

688.01 

37,668.48 

220 

48,400 

10,648,000 

14.8324 

6.0368 

.004545455 

691.15 

38,013.27 

221 

48,841 

10,793,861 

14.8661 

6.0459 

.004524887 

694.29 

38,359.63 

222 

49,284 

10,941,048 

14.8997 

6.0550 

.004504505 

697.43 

38,707.56 

223 

49,729 

11,089,567 

14.9332 

6.0641 

.004484305 

700.58 

39,057.07 

224 

50,176 

11,239,424 

14.9666 

6.0732 

.004464286 

703.72 

39,408.14 

225 

50,625 

11,390,625 

15.0000 

6.0822 

.004444444 

706.86 

39,760.78 

226 

51,076 

11,543,176 

15.0333 

6.0912 

.004424779 

710.00 

40,115.00 

227 

51,529 

11,697,083 

15.0665 

6.1002 

.004405286 

713.14 

40,470.78 

228 

51,984 

11,852,352 

15.0997 

6.1091 

.004385965 

716.28 

40,828.14 

229 

52,441 

12,008,989 

15.1327 

6.1180 

.004366812 

719.42 

41,187.07 

230 

52,900 

12,167,000 

15.1658 

6.1269 

.004347826 

722.57 

41,547.56 

231 

53,361 

12,326,391 

15.1987 

6.1358 

.004329004 

725.71 

41,909.63 

232 

53,824 

12,487,168 

15.2315 

6.1446 

.004310345 

728.85 

42,273.27 

233 

54,289 

12,649,337 

15.2643 

6.1534 

.004291845 

731.99 

42,638.48 

234 

54,756 

12,812,904 

15.2971 

6.1622 

.004273504 

735.13 

43,005.26 

235 

55,225 

12,977,875 

15.3297 

6.1710 

.004255319 

738.27 

43,373.61 

236 

55,696 

13,144,256 

15.3623 

6.1797 

.004237288 

741.42 

43,743.54 

237 

56,169 

13,312,053 

15.3948 

6.1885 

.004219409 

744.56 

44,115.03 

238 

56,644 

13,481,272 

15.4272 

6.1972 

.004201681 

747.70 

44,488.09 

239 

57,121 

13,651,919 

15.4596 

6.2058 

.004184100 

750.84 

44,862.73 

240 

57,600 

13,824,000 

15.4919 

6.2145 

.004166667 

753.98 

45,238.93 

241 

58,081 

13,997,521 

15.5242 

6.2231 

.004149378 

757.12 

45,616.71 

242 

58,564 

14,172,488 

15.5563 

6.2317 

.004132231 

760.27 

45,996.06 

243 

59,049 

14,348,907 

15.5885 

6.2403 

.004115226 

763.41 

46,376.98 

244 

59,536 

14,526,784 

15.6205 

6.2488 

.004098361 

766.55 

46,759.47 

378 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Ciroum. 

-  Area 

245 

60,025 

14,706,125 

15.6525 

6.2573 

.004081633 

769.69 

47,143.52 

246 

60,516 

14,886,936 

15.6844 

6.2658 

.004065041 

772.83 

47,529.16 

247 

61,009 

15,069,223 

15.7162 

6.2743 

.004048583 

775.97 

47,916.36 

248 

61,504 

15,252,992 

15.7480 

6.2828 

.004032258 

779.11 

48,305.13 

249 

62,001 

15,438,249 

15.7797 

6.2912 

.004016064 

782.26 

48,695.47 

250 

62,500 

15,625,000 

15.8114 

6.2996 

.004000000 

785.40 

49,087.39 

251 

63,001 

15,813,251 

15.8430 

6.3080 

.003984064 

•  788.54 

49,480.87 

252 

63,504 

16,003,008 

15.8745 

6.3164 

.0039G8254 

791.68 

49,875.92 

253 

64,009 

16,194,277 

15.9060 

6.3247 

.003952569 

794.82 

50,272.55 

254 

64,516 

16,387,064 

15.9374 

6.3330 

.003937008 

797.96 

50,670.75 

255 

65,025 

16,581,375 

15.9687 

6.3413 

.003921569 

801.11 

51,070.52 

256 

65,536 

16,777,216 

16.0000 

6.3496 

.003906250 

804.25 

51,471.85 

257 

66.049 

16,974,593 

16.0312 

6.3579 

.003891051 

807.39 

51,874.76 

258 

66,564 

17,173,512 

16.0624 

6.3661 

.003875969 

810.53 

52,279.24 

259 

67,081 

17,373,979 

16.0935 

6.3743 

.003861004 

813.67 

52,685.29 

260 

67,600 

17,576,000 

16.1245 

6.3825 

.003846154 

816.81 

53,092.92 

261 

68,121 

17,779,581 

16.1555 

6.3907 

.003831418 

819.96 

53,502.11 

262 

68,644 

17,984,728 

16.1864 

6.3988 

.003816794 

823.10 

53,'912.87 

263 

69,169 

18,191,447 

16.2173 

6.4070 

.003802281 

826.24 

54,325.21 

264 

69,696 

18,399,744 

16.2481 

6.4151 

.003787879 

829.38 

54,739.11 

265 

70,225 

18,609,625 

16.2788 

6.4232 

.003773585 

832.52 

55,154.59 

266 

70,756 

18,821,096 

16.3095 

6.4312 

.003759398 

835.66 

55,571.63 

267 

71,289 

19,034,163 

16.3401 

6.4393 

.003745318 

838.81 

55,990.25 

268 

71,824 

19,248,832 

16.3707 

6.4473 

.003731343 

841.95 

56,410.44 

269 

72,361 

19,465,109 

16.4012 

6.4553 

.003717472 

845.09 

56,832.20 

270 

72,900 

19,683,000 

16.4317 

6.4633 

.003703704 

848.23 

57,255.53 

271 

73,441 

19,902,511 

16.4621 

6.4713 

.003690037 

851.37 

57,680.43 

272 

73,984 

20,123,613 

16.4924 

6.4792 

.003676471 

854.51 

58,106.90 

273 

74,529 

20,346,417 

16.5227 

6.4872 

.003663004 

857.65 

58,534.94 

274 

75,076 

20,570,824 

16.5529 

6.4951 

.003649635 

860.80 

58,9&4.55 

275 

75,625 

20,796,875 

16.5831 

6.5030 

.003636364 

8G3.94 

59,395.74 

276 

76,176 

21,024,576 

16.6132 

6.5108 

.003623188 

867.08 

59,828.49 

277 

76,729 

21,253,933 

16.6433 

6.5187 

.003610108 

870.22 

60,262.82 

278 

77,284 

21,484,952 

16.6783 

6.5265 

.003597122 

873.36 

60,698.71 

279 

77,841 

>  21,717,639 

16.7033 

6.5343 

.003584229 

876.50 

61,136.18 

280 

78,400 

21,952,000 

16.7332 

6.5421 

.003571429 

879.65 

61,575.22 

281 

78,961 

22,188,041 

16.7631 

G.5499 

.003558719 

882.79 

62,015.82 

282 

79,524 

22,425,768 

16.7929 

6.5577 

.003546099 

885.93 

62,458.00 

283 

80,089 

22,665,187 

16.8226 

6.5654 

.003533569 

889.07 

62,901.75 

284 

80,656 

22,906,304 

16.8523 

6.5731 

.003522127 

892.21 

63,347.07 

285 

81,225 

23,149,125 

16.8819 

6.5808 

.003508772 

895.35 

63,793.97 

286 

81,796 

23,393,656 

16.9115 

6.5885 

.003496503 

898.50 

64,242.43 

287 

82,369 

23,639,903 

16.9411 

6.5962 

.003484321 

901.64 

64,692.46 

288 

82,944 

23,887,872 

16.9706 

6.6039 

.003472222 

904.78 

65,144.07 

289 

83,521 

24,137,569 

17.0000 

6.6115 

.003460208 

907.92 

65,597.24 

290 

84,100 

24,389,000 

17.0294 

6.6191 

.003448276 

911.06 

66,051.99 

291 

84,681 

24,642,171 

17.0587 

6.6267 

.003436428 

914.20 

66,508.30 

292 

85,264 

24,897,088 

17.0880 

6.6343 

.003424658 

917.35 

66,966.19 

293 

85,849 

25,153,757 

17.1172 

6.6419 

.003412969 

920.49 

67,425.65 

294 

86,436 

25,412,184 

17.1464 

6.6494 

.003401361 

923.63 

67,886.68 

295 

87,025 

25,672,375 

17.1756 

6.6569 

.003389831 

926.77 

68.349.28 

296 

87,616 

25,934,836 

17.2047 

6.6644 

.003378378 

929.91 

68,813.45 

297 

88,209 

26,198,073 

17.2337 

6.6719 

.003367003 

933.05 

69,279.19 

298 

88,804 

26,463,592 

17.2627 

6.6794 

.003355705 

936.19 

69,746.50 

299 

89,401 

26,730,899 

17.2916 

6.6869 

.003344482 

939.34 

70,215.38 

300 

90,000 

27,000,000 

17.3205 

6.6943 

.003333333 

942.48 

70,685.83 

301 

90,601 

27,270,901 

17.3494 

6.7018 

.003322259 

945.62 

71,157.86 

302 

91,204 

27,543,608 

17.3781 

6.7092 

.003311258 

948.76 

71,631.45 

303 

91,809 

27,818,127 

17.4069 

6.7166 

.003301330 

951.90 

72,106.62 

304 

92,416 

28,094,464 

17.4356 

6.7240 

.003289474 

955.04 

72,583.36 

305 

93,025 

28,372,625 

17.4642 

6.7313 

.003278689 

958.19 

73,061.66 

306 

93,636 

28,652,616 

17.4929 

6.7387 

.003267974 

961.33 

73,541.54 

307 

94,249 

28,934,443 

17.5214 

6.7460 

.003257329 

964.47 

74,022.99 

SQUARES,  CUBES,  ROOTS,  ETC. 


379 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circnm. 

Area 

308 

94,864 

29,218,112 

17.5499 

6.7533 

.003246753 

967.61 

74,506.01 

309 

95,481 

29,503,629 

17.5784 

6.7606 

.003236246 

970.75 

74,990.60 

310 

96,100 

29,791,000 

17.6068 

6.7679 

.003225806 

973.89 

75,476.76 

311 

96,721 

30,080,231 

17.6352 

6.7752 

.003215434 

977.04 

75,964.50 

312 

97,344 

30,371,328 

17.6635 

6.7824 

.003205128 

980.18 

76,453.80 

313 

97,969 

30,664,297 

17.6918 

6.7897 

.003194888 

983.32 

76,944.67 

314 

98,596 

30,959,144 

17.7200 

6.7969 

.003184713 

986.46 

77,437.12 

315 

99,225 

31,255,875 

17.7482 

6.8041 

.003174603 

989.60 

77,931.13 

316 

99,856 

31,554,496 

17.7764 

6.8113 

.003164557 

992.74 

78,426.72 

317 

100,489 

31,855,013 

17.8045 

6.8185 

.003154574 

995.88 

78,923.88 

318 

101,124 

32,157,432 

17.8326 

6.8256 

.003144654 

999.03 

79,422.60 

319 

101,761 

32,461,759 

17.8606 

6.8328 

.003134796 

1,002.17 

79,922.90 

320 

102,400 

32,768,000 

17.8885 

6.8399 

.003125000 

1,005.31 

80,424.77 

321 

103,041 

33,076,161 

17.9165 

6.8470 

.003115265 

1,008.45 

80,928.21 

322 

103,684 

33,386,248 

17.9444 

6.8541 

.003105590 

1,011.59 

81,433.22 

323 

104,329 

33,698,267 

17.9722 

6.8612 

.003095975 

1,014.73 

81,939.80 

324 

104,976 

34,012,224 

18.0000 

6.8683 

.003086420 

1,017.88 

82,447.96 

325 

105,625 

34,328,125 

18.0278 

6.8753 

.003076923 

1,021.02 

82,957.68 

326 

106,276 

34,645,976 

18.0555 

6.8824 

.003067485 

1,024.16 

83,468.98 

327 

106,929 

34,965,783 

18.0831 

6.8894 

.003058104 

1,027.30 

83,981.84 

328 

107,584 

35,287,552 

18.1108 

6.8964 

.003048780 

1,030.44 

84,496.28 

329 

108,241 

35,611,289 

18.1384 

6.9034 

.003039514 

1,033.58 

85,012.28 

330 

108,900 

35,937,000 

18.1659 

6.9104 

.003030303 

1,036.73 

85,529.86 

331 

109,561 

36,264,691 

18.1934 

6.9174 

.003021148 

1,039.87 

86,049.01 

332 

110,224 

36,594,368 

18.2209 

6.9244 

.003012048 

1,043.01 

86,569.73 

333 

110,889 

36,926,037 

18.2483 

6.9313 

.003003003 

1,046.15 

87,092.02 

334 

111,556 

37,259,704 

18.2757 

6.9382 

.002994012 

1,049.29 

87,615.88 

335 

112,225 

37.595,375 

18.3030 

6.9451 

.002985075 

1,052.43 

88,141.31 

336 

112,896 

37,933,056 

18.3303 

6.9521 

.002976190 

1,055.58 

88,668.31 

337 

113,569 

38.272,753 

18.3576 

6.9589 

.002967359 

1,058.72 

89,196.88 

338 

114,244 

38,614,472 

18.3818 

6.9658 

.002958580 

1,061.86 

89,727.03 

339 

114,921 

38,958,219 

18.4120 

6.9727 

.002949853 

1,065.00 

90,258.74 

340 

115,600 

39,304,000 

18.4391 

6.9795 

.002941176 

1,068.14 

90,792.03 

341 

116,281 

39,651,821 

18.4662 

6.9864 

.002932551 

1,071.28 

91,326.88 

342 

116,964 

40,001,688 

18.4932 

6.9932 

.002923977 

1,074.42 

91,863.31 

343 

117,649 

40,353,607 

18.5203 

7.0000 

.002915452 

1,077.57 

92,401.31 

344 

118,336 

40,707,584 

18.5472 

7.0068 

.002906977 

1,080.71 

92,940.88 

345 

119,025 

41,063,625 

18.5742 

7.0136 

.002898551 

1,083.85 

93,482.02 

346 

119,716 

41,421,736 

18.6011 

7.0203 

.002890173 

1,086.99 

94,024.73 

347 

120,409 

41,781,923 

18.6279 

7.0271 

.002881844 

1,090.13 

94,569.01 

348 

121,104 

42,144,192 

18.6548 

7.0338 

.002873563 

1,093.27 

95,114.86 

349 

121,801 

42,508,549 

18.6815 

7.0406 

.002865330 

1,096.42 

95,662.28 

350 

122,500 

42,875,000 

18.7083 

7.0473 

.002857143 

1,099.56 

96,211.28 

351 

123,201 

43,243,551 

18.7350 

7.0540 

.002849003 

1,102.70 

96,761.84 

352 

123,904 

43,614,208 

18.7617 

7.0607 

.002840909 

1,105.84 

97,313.97 

353 

124,609 

43,986,977 

18.7883 

7.0674 

.002832861 

1,108.98 

97,867.68 

354 

125,316 

44,361,864 

18.8149 

7.0740 

.002824859 

1,112.12 

98,422.96 

355 

126,025 

44,738,875 

18.8414 

7.0807 

.002816901 

1,115.27 

98,979.80 

356 

126,736 

45,118,016 

18.8680 

7.0873 

.002808989 

1,118.41 

99,538.22 

357 

127,449 

45,499,293 

18.8944 

7.0940 

.002801120 

1,121.55 

100,098.21 

358 

128,164 

45,882,712 

18.9209 

7.1006 

.002793296 

1,124.69 

100,659.77 

359 

128,881 

46,268,279 

18.9473 

7.1072 

.002785515 

1,127.83 

101,222.90 

360 

129,600 

46,656,000 

18.9737 

7.1138 

.002777778 

1,130.97 

101,787.60 

361 

130,321 

47,045,881 

19.0000 

7.1204 

.002770083 

1,134.11 

102,353.87 

362 

131,044 

47,437,928 

19.0263 

7.1269 

.002762431 

1,137.26 

102,921.72 

363 

131,769 

47,832,147 

19.0526 

7.1335 

.002754821 

1,140.40 

103,491.13 

364 

132,496 

48,228,544 

19.0788 

7.1400 

.002747253 

1,143.54 

104,062.12 

365 

133,225 

48,627,125 

19.1050 

7.1466 

.002739726 

1,146.68 

104,634.67 

366 

133,956 

49,027,896 

19.1311 

7.1531 

.002732240 

1,149.82 

105,208.80 

367 

134,689 

49,430,863 

19.1572 

7.1596 

.002724796 

1,152.96 

105,784.49 

368 

135,424 

49,836,032 

19.1833 

7.1661 

.002717391 

1,156.11 

106,361.76 

369 

136,161 

50,243,409 

19.2094 

7.1726 

.002710027 

1,159.25 

106,940.60 

370 

136,900 

50,653,000 

19.2354 

7.1791 

.002702703 

1,162.39 

107,521.01 

380 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum 

Area 

371 

137,641 

51,064,811 

19.2614 

7.1855 

.002695418 

1,165.53 

108,102.99 

372 

138,384 

51,478,848 

19.2873 

7.1920 

.002688172 

1,168.67 

108,686.54 

373 

139,129 

51,895,117 

19.3132 

7.1984 

.002680965 

1,171.81 

109,271.66 

374 

139,876 

52,313,624 

19.3391 

7.2048 

.002673797 

1,174.96 

109,858.35 

375 

140,625 

52,734,375 

19.3649 

7.2112 

.002666667 

1,178.10 

110,446.62 

376 

141,376 

53,157,376 

19.3907 

7.2177 

.002659574 

1,181.24 

111,036.45 

377 

142,129 

53,582,633 

19.4165 

7.2240 

.002652520 

1,184.38 

111,627.86 

378 

142,884 

64,010,152 

19.4422 

7.2304 

.002645503 

1,187.52 

112,220.83 

379 

143,641 

54,439,939 

19.4679 

7.2368 

.002638521 

1,190.66 

112,815.38 

380 

144,400 

54,872,000 

19.4936 

7.2432 

.002631579 

1,193.81 

113,411.49 

381 

145,161 

55,306,341 

19.5192 

7.2495 

.002624672 

1,196.95 

114,009.18 

382 

145,924 

55,742,968 

19.54-18 

7.2558 

.002617801 

1,200.09 

114,608.44 

383 

146,689 

56,181,887 

19.5704 

7.2022 

.002610966 

1,203.23 

115,209.27 

384 

147,456 

56,623.104 

19.5959 

7.2G85 

.002604167 

1,200.37 

115,811.67 

385 

148,225 

57,066,625 

19.6214 

7.2748 

.002597403 

1,209.51 

116,415.64 

386 

148,996 

57,512,456 

19.64G9 

7.2811 

.002590674 

1,212.65 

117,021.18 

387 

149,769 

57,960,603 

19.6723 

7.2874 

.002583979 

1,215.80 

117,628.30 

388 

150,544 

58,411,072 

19.6977 

7.2936 

.002577320 

1,218.94 

118,236.98 

389 

151,321 

58,863,869 

19.7231 

7.2999 

.002570694 

1,222.08 

118,847.24 

390 

152,100 

59,819,000 

19.7484 

7.3061 

.002564103 

1,225.22 

119,459.06 

391 

152,881 

59,776,471 

19.7737 

7.3124 

.002557545 

1,228.36 

120,072.46 

392 

153,664 

60,236,288 

19.7990 

7.3186 

.002551020 

1,231.50 

120,687.42 

393 

154,449 

60,698,457 

19.8242 

7.3248 

.002544529 

1,234.65 

121,303.96 

394 

155,236 

61,162,984 

19.8494 

7.3310 

.002538071 

1,237.79 

121,922.07 

395 

156,025 

61,629,875 

19.8746 

7.3372 

.002531646 

1,240.93 

122,541.75 

396 

156,816 

62,099,136 

19.8997 

7.3434 

.002525253 

1,244.07 

123,163.00 

397 

157,609 

62,570,773 

19.9249 

7.3496 

.002518892 

1,247.21 

123,785.82 

398 

158,404 

63,044,792 

19.9499 

7.3558 

.002512563 

1,250.35 

124,410.21 

399 

159,201 

63,521,199 

19.9750 

7.3619 

.002506266 

1,253.50 

125,036.17 

400 

160,000 

64,000,000 

20.0000 

7.3681 

.002500000 

1,256.64 

125,663.71 

401 

160,801 

64,481,201 

20.0250 

7.3742 

.002493766 

1,259.78 

126,292.81 

402 

161,604 

64,964,808 

20.0499 

7.3803 

.002487562 

1,262.92 

126,923.48 

403 

162,409 

65,450,827 

20.0749 

7.3864 

.002481390 

1,266.06 

127,555.73 

404 

163,216 

65,939,264 

20.0998 

7.3925 

.002475248 

1,269.20 

128,189.55 

405 

164,025 

66,430,125 

20.1246 

7.3986 

.002469136 

1.272.35 

128,824.93 

406 

164,836 

66,923,416 

20.1494 

7.4047 

.002463054 

1,275.49 

129,461.89 

407 

165,649 

67,419,143 

20.1742 

7.4108 

.002457002 

1,278.63 

130,100.42 

408 

166,464 

67,917,312 

20.1990 

7.4169 

.002450980 

1,281.77 

130,740.52 

409 

167,281 

68,417,929 

20.2237 

7.4229 

.002444988 

1,284.91 

131,382.19 

410 

168,100 

68,921,000 

20.2485 

7.4290 

.002439024 

1,288.05 

132,025.43 

411 

168,921 

69,426,531 

20.2731 

7.4350 

.002433090 

1,291.19 

132,670.24 

412 

169,744 

69,934,528 

20.2978 

7.4410 

.002427184 

1,294.34 

133,316.63 

413 

170,569 

70,444,997 

20.3224 

7.4470 

.002421308 

1,297.48 

133,964.58 

414 

171,396 

70,957,944 

20.3470 

7.4530 

.002415459 

1,300.62 

134,614.10 

415 

172,225 

71,473,375 

20.3715 

7.4590 

.002409639 

1,303.76 

135,265.20 

416 

173,056 

71,991,296 

20.3961 

7.4650 

.002406846 

,306.90 

135,917.86 

417 

173,889 

72,511,713 

20.4206 

7.4710 

.002398082 

,310.04 

136,572.10 

418 

174,724 

73,034,632 

20.4450 

7.4770 

.002392344 

,313.19 

137,227.91 

419 

175,561 

73,560,059 

20.4G95 

7.4829 

.002386635 

,316.33 

137,885.29 

420 

176,400 

74,088,000 

20.4939 

7.4889 

.002380952 

,319.47 

38,544.24 

421 

177,241 

74,618,461 

20.5183 

7.4948 

.002375297 

,322.61 

39,204.76 

422 

178,084 

75,151,448 

20.5426 

7.5007 

.002369668 

,325.75 

39,866.85 

423 

178,929 

75,686,967 

20.5670 

7.5067 

.002364066 

,328.89 

40,530.51 

424 

179,776 

76,225,024 

20.5913 

7.5126 

.002358491 

,332.04 

41,195.74 

425 

180,625 

76,765,625 

20.6155 

7.5185 

.002352941 

,335.18 

41,862.54 

426 

181,476 

77,308,776 

20.6398 

7.5244 

.002347418 

,338.32 

42,530.92 

427 

182,329 

77,a54,483 

20.6640 

7.5302 

.002341920 

,341.46 

43,200.86 

428 

183,184 

78,402,752 

20.6882 

7.5361 

.002336449 

,344.60 

43,872.38 

429 

184,041 

78,953,589 

20.7123 

7.5420 

.002331002 

,347.74 

44,545.46 

430 

184,900 

79,507,000 

20.7364 

7.5478 

.002325581 

,350.88 

45,220.12 

431 

185,761 

80,062,991 

20.7605 

7.5537 

.002320186 

,354.03 

45.896.35 

432 

186,624 

80,621,568 

20.7846 

7.5595 

.002314815 

,357.17 

46,574.15 

433 

187,489 

81,182,737 

20.8087 

7.5654 

.002309469 

,360.31 

47,253.52 

SQUARES,  CUBES,  ROOTS,  ETC. 


381 


No. 

Square 

Cube 

Sq.  Boot 

Cu.  Root 

Reciprocal 

Circum. 

Area 

434 

188,356 

81,746,504 

20.8327 

7.5712 

.002304147 

1,363.45 

147,934.46 

435 

189,225 

82,312,875 

20.8567 

7.5770 

.002298851 

1,366.59 

148,616.97 

436 

190,0% 

82,881,856 

20.8806 

7.5828 

.002293578 

1,369.73 

149,301.05 

437 

190,969 

83,453,453 

20.9045 

7.5886 

.002288330 

1,372.88 

149,986.70 

466 

191,844 

84,027,672 

U0.92S1 

7.5944 

.002283105 

1,376.02 

150,673.93 

439 

192,721 

84,604,519 

20.9523 

7.6001 

.002277904 

1,379.16 

151,362.72 

440 

193,600 

85,184,000 

20.9762 

7.6059 

.002272727 

1,382.30 

152,053,08 

441 

194,481 

85,766,121 

UUKXJO 

7.6117 

.002267574 

1,385.44 

152,745.02 

442 

195,364 

86,350,888 

21.0238 

7.6174 

.002262443 

1,388.58 

153,438.53 

443 

196,249 

86,938,307 

21.0476 

7.6232 

.002257336 

1,391.73 

154,133.60 

444 

197,136 

87,528,384 

21.0713 

7.6289 

.002252252 

1,394.87 

154,830.25 

445 

198,025 

88,121,125 

21.0950 

7.6346 

.002247191 

1,398.01 

155,528.47 

446 

198,916 

88,716,536 

21.1187 

7.6403 

.002242152 

1,401.15 

156,228.26 

447 

199,809 

89,314,623 

21.1424 

7.6460 

.002237136 

1,404.29 

156,929.62 

448 

200,704 

89,915,392 

21.1660 

7.6517 

.002232143 

1,407.43 

157,632.55 

449 

201,601 

90,518,849 

21.1896 

7.6574 

.002227171 

1,410.58 

158,337.06 

450 

202,500 

91,125,000 

21.2132 

7.6631 

.002222222 

1,413.72 

159,043.13 

451 

203,401 

91,733,851 

21.2368 

7.6688 

.002217295 

1,416.86 

159,750.77 

452 

204,304 

92,345,408 

21.2603 

7.6744 

.002212389 

1,420.00 

160,459.99 

453 

205,209 

92,959,677 

21.2838 

7.6801 

.002207506 

1,423.14 

161,170.77 

454 

206,116 

93,576,664 

21.3073 

7.6857 

.002202643 

1,426.28 

161,883.13 

455 

207,025 

94,196,375 

21.3307 

7.6914 

.002197802 

1,429.42 

162,597.05 

456 

207,936 

94,818,816 

21.3542 

7.6970 

.002192982 

1,432.57 

163,312.55 

457 

208,849 

95,443,993 

21.3776 

7.7026 

.002188184 

1,435.71 

164,029.62 

458 

209,764 

96,071,912 

21.4009 

7.7082 

.002183406 

1,438.85 

164,748.26 

459 

210,681 

96,702,579 

21.4213 

7.7188 

.002178649 

1,441.99 

165,468.47 

460 

211,600 

97,336,000 

21.4476 

7.7194 

.002173913 

1,445.13 

166,190.25 

461 

212,521 

97,972,181 

21.4709 

7.7250 

.002169197 

1,448.27 

166,913.60 

462 

213,444 

98,611,128 

21.4942 

7.7306 

.002164502 

1,451.42 

167,638.53 

463 

214,369 

99;252,847 

21.5174 

7.7362 

.002159827 

1,454.56 

168,365.02 

464 

215,296 

99,897,344 

21.5407 

7.7418 

.002155172 

1,457.70 

169,093.08 

465 

216,225 

100,544,625 

21.5639 

7.7473 

.002150538 

1,460.84 

169,822.72 

466 

217,156 

101,194,696 

21.5870 

7.7529 

.002145923 

1,463.98 

170,553.92 

467 

218,089 

101,847,563 

21.6102 

7.7584 

.002141328 

1,467.12 

171,286.70 

468 

219,024 

102,503,232 

21.6333 

7.7639 

.002136752 

1,470.27 

172,021.05 

469 

219,961 

103,161,709 

21.6564 

7.7695 

.002132196 

1,473.41 

172,756.97 

470 

220,900 

103,823,000 

21.6795 

7.7750 

.002127660 

1,476.55 

173,494.45 

471 

221,841 

104,487,111 

21.7025 

7.7805 

.002123142 

1,479.69 

174,233.51 

472 

222,784 

105,154,048 

21.7256 

7.7860 

.002118644 

1,482.83 

174,974.14 

473 

223,729 

105,823,817 

21.7486 

7.7915 

.002114165 

1,485.97 

175,716.35 

474 

224,676 

106,496,424 

21.7715 

7.7970 

.002109705 

1,489.11 

176,460.12 

475 

225,625 

107,171,875 

21.7945 

7.8025 

.002105263 

1,492.26 

177,205.46 

476 

226,576 

107,850,176 

21.8174 

7.8079 

.002100840 

1,495.40 

177,952.37 

477 

227,529 

108,531,333 

21.8403 

7.8134 

.002096486 

1,498.54 

178,700.86 

478 

228,484 

109,215,352 

21.8632 

7.8188 

.002092050 

1,501.68 

179,450.91 

479 

229,441 

109,902,239 

21.8861 

7.8243 

.002087683 

1,504.82 

180,202.54 

480 

230,400 

110,592,000 

21.9089 

7.8297 

.002083333 

1,507.96 

180,955.74 

481 

231,361 

111,284,641 

21.9317 

7.8352 

.002079002 

1,511.11 

181,710.50 

482 

232,324 

111,980,168 

21.9545 

7.8406 

.002074689 

1,514.25 

182,466.84 

483 

233,289 

112,678,587 

21.9775 

7.8460 

.002070393 

1.517.39 

183,224.75 

484 

234,256 

113,379,904 

22.0000 

7.8514 

.002066116 

1,520.53 

183,984.23 

485 

235,225 

114,084,125 

22.0227 

7.8568 

.002061856 

1,523.67 

184,745.28 

486 

236,196 

114,791,256 

22.0454 

7.8622 

.002057613 

1,526.81 

185,507.90 

487 

237,169 

115,501,303 

22.0681 

7.8676 

.002053388 

1,529.96 

186,272.10 

488 

238,144 

116,214,272 

22.0907 

7.8730 

.002049180 

1,533.10 

187,037.86 

489 

239,121 

116,930,169 

22.1133 

7.8784 

.002044990 

1,536.24 

187,805.19 

490 

240,100 

117,649,000 

22.1359 

7.8837 

.002040816 

1,539.38 

188,574.10 

491 

241,081 

118,370,771 

22.1585 

7.8891 

.002036660 

1,542.52 

189,344.57 

492 

242,064 

119,095,488 

22.1811 

7.8944 

.002032520 

1,545.66 

190,116.62 

493 

243.049 

119,823,157 

22.2036 

7.8998 

.002028398 

1,548.81 

190,890.24 

494 

244,036 

120,553,784 

22.2261 

7.9051 

.002024291 

1,551.95 

191,665.43 

495 

245,025 

121,287,375 

22.2486 

7.9105 

.002020292 

1,555.09 

192,442.18 

496 

246,016 

122,023,936 

22.2711 

7.9158 

.002016129 

1,558.23 

193,220.51 

382 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Boot 

Reciprocal 

Circom. 

Area 

497 

247,009 

122,763,473 

22.2935 

7.9211 

.002012072 

1,561.37 

194,000.41 

498 

248,004 

123,505,992 

22.3159 

7.9264 

.002008032 

1,564.51 

194,781.89 

499 

249,001 

124,251,499 

22.3383 

7.9317 

.002004008 

1,567.65 

195,564.93 

500 

250,000 

125,000,000 

22.3607 

7.9370 

.002000000 

1,570.80 

196,349.54 

501 

251,001 

125,751,501 

22.3830 

7.9423 

.001996008 

1,573.94 

197,135.72 

502 

252,004 

126,506,008 

22,4054 

7.9476 

.001992032 

1,577.08 

197,923.48 

503 

253,009 

127,263,527 

22.4277 

7.9528 

.001988072 

1,580.22 

198,712.80 

504 

254,016 

128,024,064 

22.4499 

7.9581 

.001984127 

1,583.36 

199,503.70 

505 

255,025 

128,787,625 

22.4722 

7.9634 

.001980198 

1,586.50 

200,296.17 

506 

256,036 

129,554,216 

22.4944 

7.9686 

.001976285 

1,589.65 

201,090.20 

507 

257,049 

130,323,843 

22.5167 

7.9739 

.001972387 

1,592.79 

201,885.81 

508 

258,064 

131,096,512 

22.5389 

7.9791 

.001968504 

1,595.93 

202,682.99 

509 

259,081 

131,872,229 

22.5610 

7.9843 

.001964637 

1,599.07 

203,481.74 

510 

260,100 

132,651,000 

22.5832 

7.9895 

.001960785 

1,602.21 

204,282.06 

511 

261,121 

133,432,831 

22.6053 

7.9948 

.001956947 

1,605.35 

205,083.95 

512 

262,144 

134,217,728 

22.6274 

8.0000 

.001953125 

1,608.50 

205,887.42 

513 

263,169 

135,005,697 

22.6495 

8.0052 

.001949318 

1,611.64 

206,692.45 

514 

264,196 

135,796,744 

22.6716 

8.0104 

.001945525 

1,614.78 

207,499.05 

515 

265,225 

136,590,875 

22.6936 

8.0156 

.001941748 

1,617.92 

208,307.23 

516 

266,256 

137,388,096 

22.7156 

8.0208 

.001937984 

1,621.06 

209,116.97 

517 

267,289 

138,188,413 

22.7376 

8.0260 

.001934236 

1,624.20 

209,928.29 

518 

268,324 

138,991,832 

22.7596 

8.0311 

.001930502 

1,627.34 

210,741.18 

519 

269,361 

139,798,359 

22.7816 

8.0363 

.001926782 

1,630.49 

211,555.63 

520 

270,400 

140,608,000 

22.8035 

8.0415 

.001923077 

1,633.63 

212,371.66 

521 

271,411 

141,420,761 

22.8254 

8.0466 

.001919386 

1,636.77 

213,189.26 

522 

272,484 

142,236,648 

22.8473 

8.0517 

.001915709 

1,639.91 

214,008.43 

523 

273,529 

143,055,667 

22.8692 

8.0569 

.001912046 

1,643.05 

214,829.17 

524 

274,576 

143,877,824 

22.8910 

8.0620 

.001908397 

1,646.19 

215,651.49 

525 

275,625 

144,703,125 

22.9129 

8.0671 

.001904762 

1,649.34 

216,475.37 

526 

276,676 

145,531,576 

22.9347 

8.0723 

.001901141 

1,652.48 

217,300.82 

527 

277,729 

146,363,183 

22.9565 

8.0774 

.001897533 

1,655.62 

218,127.85 

528 

278,784 

147,197,952 

22.9783 

8.0825 

.001893939 

1,658.76 

218,956.44 

529 

279,841 

148,035,889 

23.0000 

8.0876 

.001890359 

1,661.90 

219,786.61 

530 

280,900 

148,877,001 

23.0217 

8.0927 

.001886792 

1,665.04 

220,618.34 

531 

281,961 

149,721,291 

23.0434 

8.0978 

.001883239 

1,668.19 

221,451.65 

532 

283,024 

150,568,768 

23.0651 

8.1028 

.001879699 

1,671.33 

222,286.53 

533 

284,089 

151,419,437 

23.0868 

8.1079 

.001876173 

1,674.47 

223,122.98 

534 

285,156 

152,273,304 

23.1084 

8.1130 

.001872659 

1,677.61 

223,961.00 

535 

286,225 

153,130,375 

23.1301 

8.1180 

.001869159 

1,680.75 

224,800.59 

536 

287,296 

153,990,656 

23.1517 

8.1231 

.001865672 

1,683.89 

225,641.75 

537 

288,369 

154,854,153 

23.1733 

8.1281 

.001862197 

1,687.04 

226,484.48 

538 

289,444 

155,720,872 

23.1948 

8.1332 

.001858736 

1,690.18 

227,328.79 

539 

290,521 

156,590,819 

23.2164 

8.1382 

.001855288 

1,693.32 

228,174.66 

540 

291,600 

157,464,000 

23.2379 

8.1433 

.001851852 

1,696.46 

229,022.10 

541 

292,681 

158,340,421 

23.2594 

8.1483 

.001848429 

1,699.60 

229,871.12 

542 

293,764 

159,220,088 

23.2809 

8.1533 

.001845018 

1,702.74 

230,721.71 

543 

294,849 

160,103,007 

23.3024 

8.1583 

.001841621 

1,705.88 

231,573.86 

544 

295,936 

160,989,184 

23.3238 

8.1633 

.001838235 

1,709.03 

232,427.59 

545 

297,025 

161,878,625 

23.3452 

8.1683 

.001834862 

1,712.17 

233.2S2.89 

546 

298,116 

162,771,336 

23.3666 

8.1733 

.001831502 

1,715.31 

234,139.76 

547 

299,209 

163,667,323 

23.3880 

8.1783 

.001828154 

1,718.45 

234,998.20 

548 

300,304 

164,566,592 

23.4094 

8.1833 

.001824818 

1,721.59 

235,858.21 

549 

301,401 

165,469,149 

23.4307 

8.1882 

.001821494 

1,724.73 

236,719.79 

550 

302,500 

166,375,000 

23.4521 

8.1932 

.001818182 

1,727.88 

237,582.94 

551 

303,601 

167,284,151 

23.4734 

8.1982 

.001814882 

1,731.02 

238,447.67 

552 

304,704 

168,196,608 

23.4947 

8.2031 

.001811594 

1,734.16 

239,313.96 

553 

305,809 

169,112,377 

23.5160 

8.2081 

.001808318 

1,737.30 

240,181.83 

554 

306,916 

170,031,464 

23.5372 

8.2130 

.001805054 

1,740.44 

241,051.26 

555 

308,025 

170,953,875 

23.5584 

8.2180 

.001801802 

1,743.58 

241,922.27 

556 

309,136 

171,879,616 

23.5797 

8.2229 

.001798561 

1,746.73 

242,794.85 

557 

310,249 

172,808,693 

23.6008 

8.2278 

.001795332 

1,749.87 

243,668.99 

558 

311,364 

173,741,112 

23.6220 

8.2327 

.001792115 

1,753.01 

244,544.71 

559 

312,481 

174,676,879 

23.6432 

8.2377 

.001788909 

1,756.15 

245,422.00 

SQUARES,  CUBES,  ROOTS,  ETC. 


383 


No 

Square 

Cube 

Sq.  Roo 

Cu.  Roo 

Reciprocal 

Circum 

Area 

560 

313,600 

175,616,000 

23.664 

8.2426 

.001785714 

1,759.2 

246,300.86 

561 

314,721 

176,558,481 

23.6854 

8.2475 

.001782531 

1,762.4 

247,181.30 

562 

315,844 

177,504,328 

23.706 

8.2524 

.001779359 

1,765.5 

248,063.30 

563 

316,969 

178,453,547 

23.7276 

8.2573 

.001776199 

1,768.7 

248,946.87 

564 

318,096 

179,406,144 

23.7487 

8.2621 

.001773050 

1,771.8 

249,832.01 

565 

319,225 

180,362,125 

23.7697 

8.2670 

.001769912 

1,775.0 

250,718.73 

566 

32o!:!f>6 

181,321,496 

23.7908 

8.2719 

.001766784 

1,778.14 

251,607.01 

567 

321,489 

182,284,263 

23.8118 

8.2768 

.001763668 

1,781.28 

252,496.87 

568 

322,624 

183,250,432 

23.8328 

8.2816 

.001760563 

1,784.42 

253,388.30 

569 

323,761 

184,220,009 

23.8537 

8.2865 

.001757469 

1,787.57 

254,281.29 

570 

324,900 

185,193,000 

23.8747 

8.2913 

.001754386 

1,790.71 

255,175.86 

571 

326,041 

186,169,411 

23.8956 

8.2962 

.001751313 

1,793.85 

256,072.00 

572 

327,184 

187,149,248 

23.9165 

8.3010 

.001748252 

1,796.99 

256,969.71 

573 

328,329 

188,132,517 

23.9374 

8.3059 

.001745201 

1,800.13 

257,868.99 

574 

:wy,476 

189,119,224 

23.9583 

8.3107 

.001742164 

1,803.27 

258,769.85 

575 

330,625 

190,109,375 

23.9792 

8.3155 

.001739130 

1,806.42 

259,672.27 

576 

331,776 

191,102,976 

24.0000 

8.3203 

.001736111 

1,809.56 

260,576.26 

577 

332,929 

192,100,033 

24.0208 

8.3251 

.001733102 

1,812.70 

261,481.83 

578 

334,084 

193,100,552 

24.0416 

8.3300 

.001730104 

,815.84 

262,388.96 

579 

335,241 

194,104,539 

24.0624 

8.3348 

.001727116 

,818.98 

63,297.67 

580 

336,400 

195,112,000 

24.0832 

8.3396 

.001724138 

,822.12 

64,207.94 

581 

337,561 

196,122,941 

24.1039 

8.3443 

.001721170 

,825.27 

65,119.79 

582 

338,724 

197,137,368 

24.1247 

8.3491 

.001718213 

,828.41 

66,033.21 

583 

339,889 

198,155,287 

24.1454 

8.3539 

.001715266 

,831.55 

66,948.20 

584 

341,056 

199,176,704 

24.1661 

8.3587 

.001712329 

,834.69 

67,864.76 

585 

342,225 

200,201,625 

24.1868 

8.3634 

.001709402 

,837.83 

68,782.89 

586 

343,396 

201,230,056 

24.2074 

8.3682 

.001706485 

840.97 

69,702.59 

587 

344,569 

202,262,003 

24,2281 

8.3730 

.001703578 

844.11 

70,623.86 

588 

345,744 

203,297,472 

24.2487 

8.3777 

.001700680 

847.26 

71,546.70 

589 

346,921 

204,336,469 

24.2693 

8.3825 

.001697793 

850.40 

72,471.12 

590 

348,100 

205,379,000 

24.2899 

8.3872 

.001694915 

853.54 

73,397.10 

591 

349,281 

206,425,071 

24.3105 

8.3919 

001692047 

856.68 

74,324.66 

592 

350,464 

207,474,688 

24.3311 

8.3967 

001689189 

859.82 

75,253.78 

593 

351,649 

208,527,857 

24.3516 

8.4014 

001686341 

862.96 

76,184.48 

594 

352,836 

209,584,584 

24.3721 

8.4061 

001683502 

866.11 

77,116.75 

595 

354,025 

210,644,875 

24.3926 

8.4108 

001680672 

869.25 

78,050.58 

596 

355,216 

211,708,736 

24.4131 

8.4155 

001677852 

872.39 

78,985.99 

597 

356,409 

212,776,173 

24.4336 

8.4202 

001675042 

875.53 

279,922.97 

598 

357,604 

213,847,192 

24.4540 

8.4249 

001672241 

878.67 

280,861.52 

599 

358,801 

214,921,799 

24.4745 

8.4296 

001669449 

881.81 

281,801.65 

600 

360,000 

216,000,000 

24.4949 

8.4343 

001C66667 

884.96 

82,743.34 

601 

361,201 

217,081,801 

24.5153 

8.4390 

001663894 

888.10 

283,686.60 

602 

362,404 

218,167,208 

4.5357 

8.4437 

001661130 

891.24 

284,631.44 

603 

363,609 

219,256,227 

4.5561 

8.4484 

001658375 

894.38 

-85,577.84 

604 

364,816 

220,348,864 

24.5764 

8.4530 

001655629 

897.52 

-86,525.82 

605 

366,025 

221,445,125 

4.5968 

8.4577 

001652893 

900.66 

-87,475.36 

606 

367,236 

222,545,016 

24.6171 

8.4623 

001650165 

903.81 

-88,426.48 

607 

368,449 

223,648,543 

4.6374 

8.4670 

001647446 

906.95 

-89,379.17 

608 

369,664 

224,755,712 

24.6577 

8.4716 

001644737 

910.09 

>90,333.43 

609 

370,881 

225,866,529 

4.6779 

8.4763 

001642036 

913.23 

1,289.26 

610 

372,100 

226,981,000 

24.6982 

8.4809 

001639344 

916.37 

2,246.66 

611 

373,321 

228,099,131 

4.7184 

8.4856 

001G36661 

919.51 

3,205.63 

612 

374,544 

229,220,928 

4.7386 

8.4902 

001633987 

922.65 

94,166.17 

613 

375,769 

230,346,397 

24.7588 

8.4948 

001631321 

925.80 

5,128.28 

614 

376,996 

231,475,544 

4.7790 

8.4994 

001628664 

928.94 

6,091.97 

615 

378,225 

232,608,375 

4.7992 

8.5040 

001626016 

932.08 

7,057.22 

616 

379.456 

233,744,896 

4.8193 

8.5086 

001623377 

935.22 

8,024.05 

617 

380,689 

234,885,113 

24.8395 

8.5132 

001620746 

938.36 

8,992.44 

618 

381,924 

236,029,032 

4.8596 

8.5178 

001618123 

941.50 

9,962.41 

619 

383,161 

237,176,659 

24.8797 

8.5224 

001615509 

944.65 

00,933.95 

620 

384,400 

238,325,000 

4.8998 

8.5270 

001612903 

947.79 

1,907.05 

621 

385,641 

239,483,061 

24.9199 

8.5316 

001610306 

950.93 

2,881.73 

622 

386S884 

240,641,848 

24.9399 

8.5362 

001607717 

954.07 

3,857.98 

384 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Boot 

Cu.Root 

Reciprocal 

Circum 

Area 

623 

388,129 

241,804,367 

24.9600 

8.5408 

.001605136 

1,957.21 

304,835.80 

624 

389,376 

242,970,624 

24.9800 

8.5453 

.001602564 

1,960.35 

305,815.20 

625 

390,625 

244,140,625 

25.0000 

8.5499 

.001600000 

1,963.50 

306,796.16 

626 

391,876 

245,314,376 

25.0200 

8.5544 

.001597444 

1,966.64 

307,778.69 

627 

393,129 

246,491,883 

25.0400 

8.5589 

.001594896 

1,969.78 

308,762.79 

628 

394,384 

247,673,152 

25.0599 

8.5635 

.001592357 

1,972.92 

309,748.47 

629 

395,641 

248,858,189 

25.0799 

8.5681 

.001589825 

l,976.0f 

310,735.71 

630 

396,900 

250,047,000 

25.0998 

8.5726 

.001587302 

1,979.20 

311,724.53 

631 

398,161 

251,239,591 

25.1197 

8.5772 

.001584786 

1,982.35 

312,714.92 

632 

399,424 

252,435,968 

25.1396 

8.5817 

.001582278 

1,985.49 

313,706.88 

633 

400,689 

233,636,137 

25.1595 

8.5862 

.001579779 

1,988.63 

314,700.40 

634 

401,956 

254,840,104 

25.1794 

8.5907 

.001577287 

1,991.77 

315,695.50 

635 

403,225 

256,047,875 

25.1992 

8.5952 

.001574803 

1,994.91 

316,692.17 

636 

404,496 

257,259,456 

25.2190 

8.5997 

.001572327 

1,998.05 

317,690.42 

637 

405,769 

258,474,853 

25.2389 

8.6043 

.001569859 

2,001.19 

318,690.23 

638 

407,044 

259,694,072 

25.2587 

8.G088 

.001567398 

2,004.34 

319,691.61 

639 

408,321 

260,917,119 

25.2784 

8.G132 

.001564945 

2,007.48 

320,694.56 

640 

409,600 

262,144,000 

25.2982 

8.6177 

.001562500 

2,010.62 

321,699.09 

641 

410,881 

263,374,721 

25.3180 

8.6222 

.0015GOOG2 

2,013.76 

322.705.18 

642 

412,164 

264,609,288 

25.3377 

8.6267 

.001557632 

2,016.90 

323,712.85 

643 

413,449 

265,847,707 

25.3574 

8.G312 

.001555210 

2,020.04 

324,722.09 

644 

414,736 

267,089,984 

25.3772 

8.6357 

.001552795 

2,023.19 

325,732.89 

645 

416,125 

268,336,125 

25.3969 

8.6401 

.001550388 

2,026.33 

326,745.27 

646 

417,316 

269,585,136 

25.4165 

8.6446 

.001547988 

2,029.47 

327,759.22 

647 

418,609 

270,840,023 

25.4362 

8.G490 

.001545595 

2,032.61 

328,774.74 

648 

419,904 

272,097,792 

25.4558 

8.G535 

.001543210 

2,035.75 

329,791.83 

649 

421,201 

273,359,449 

25.4755 

8.6579 

.001540832 

2,038.89 

330,810.49 

650 

422,500 

274,625,000 

25.4951 

8.6624 

.0015384G2 

2,042.04 

331,830.72 

651 

423,801 

275,894,451 

25.5147 

8.6668 

.001536098 

2,045.18 

332,852.53 

652 

425,104 

277,167,808 

25.5343 

8.6713 

.001533742 

2,048.32 

333",875.90 

653 

426,409 

278,445,077 

25.5539 

8.6757 

.001531394 

2,051.46 

334,900.85 

654 

427,716 

279,726,264 

25.5734 

8.6801 

.001529052 

2,054.60 

335,927.36 

655 

429,025 

281,011,375 

25.5930 

8.6845 

.001526718 

2,057.74 

336,955.45 

656 

430,336 

282,300,416 

25.6125 

8.6890 

.00152-1390 

2,060.88 

337,985.10 

657 

431,639 

283,593,393 

25.6320 

8.6934 

.001522070 

2,064.03 

339,016.33 

658 

432,964 

284,890,312 

25.6515 

8.6978 

.001519751 

2,OG7.17 

340,049.13 

659 

434,281 

286,191,179 

25.6710 

8.7022 

.001517451 

2,070.31 

341,083.50 

660 

435,600 

287,496,000 

25.C905 

8.7066 

.001515152 

2,073.45 

42,119.44 

661 

436,921 

288,804,781 

25.7099 

8.7110 

.001512859 

2,076.59 

343,156.95 

662 

438,244 

290,117,528 

25.7294 

8.7154 

.001510574 

2,079.73 

344,196.03 

663 

439,569 

291,434,247 

25.7488 

8.7198 

.001508296 

,082.88 

45,236.69 

664 

440,896 

292,754,944 

25.7682 

8.7241 

.001506024 

,086.02 

46,278.91 

665 

442,225 

294,079,625 

25.7876 

8.7285 

.001503759 

,089.16 

47,322.70 

666 

443,556 

295,408,296 

25.8070 

8.7329 

.001501502 

,092.30 

48,368.07 

667 

444,899 

296,740,963 

25.8263 

8.7373 

.001499250 

,095.44 

349,415.00 

668 

446,224 

298,077,632 

25.8457 

8.7416 

.001497006 

,098.58 

50,463.51 

669 

447,561 

299,418,309 

25.8650 

8.7460 

.001494768 

,101.73 

51,513.59 

670 

448,900 

300,763,000 

25.8844 

8.7503 

.001492537 

,104.87 

52,565.24 

671 

450,241 

302,111,711 

25.9037 

8.7547 

.001490313 

,108.01 

53,618.45 

672 

451,584 

303,464,448 

25.9230 

8.7590 

.001488095 

,111.15 

54,673.21 

673 

452,929 

304,821,217 

25.9422 

8.7634 

.001485884 

,114.29 

55,729.60 

674 

454,276 

306,182,024 

25.9615 

8.7677 

.001483680 

,117.43 

56,787.54 

675 

455,625 

307,546,875 

25.9808 

8.7721 

.001481481 

,120.58 

57,847.04 

676 

456,976 

308,915,776 

26.0000 

8.7764 

.001479290 

,123.72 

58,908.11 

677 

458,329 

310,288,733 

26.0192 

8.7807 

.001477105 

,126.86 

59,970.75 

678 

459,684 

311,665,752 

26.0384 

8.7850 

.001474926 

,130.00 

61,034.97 

679 

461,041 

313,046,839 

26.0576 

8.7893 

.001472754 

,133.14 

62,100.75 

680 

462,400 

314,432,000 

26.0768 

8.7937 

.001470588 

,136.28 

63,168.11 

681 

463,761 

315,821,241 

26.0960 

8.7980 

.001468429 

,139.42 

64,237.04 

682 

465,124 

317,214,568 

26.1151 

8.8023 

.001466276 

,142.57 

65,307.54 

683 

466,489 

318,611,987 

26.1343 

8.8066 

.001464129 

,145.71 

66,379.60 

684 

467,856 

320,013,504 

26.1534 

8.8109 

.001461988 

148.85 

67,453.24 

685 

469,225 

321,419,125 

26.1725 

8.8152 

.001459854 

151.99 

68,528.45 

SQUARES,  CUBES,  ROOTS,  ETC, 


385 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Are* 

686 

470,596 

322,828,856 

26.1916 

8.8194 

.001457726 

2,155.13 

369,605.23 

687 

471,969 

324,242,703 

26.2107 

8.8237 

.001455604 

2,158.27 

370,683.59 

688 

473,344 

325,660,672 

26.2298 

8.8280 

.001453488 

2,161.42 

371,763.51 

689 

474,721 

327,082,769 

26.2488 

8.8323 

.001451379 

2,164.56 

372,845.00 

690 

476,100 

328,509,000 

26.2679 

8.8366 

.001449275 

2,167.70 

373,928.07 

691 

477,481 

329,939,371 

26.2869 

8.8408 

.001447178 

2,170.84 

375,012.70 

692 

47,s!sW 

331,373,888 

26.3059 

8.8451 

.001445087 

2,173.98 

376,098.91 

693 

480,249 

332,812,557 

2G.3249 

8.8493 

.001443001 

2,177.12 

377,186.68 

694 

481,636 

334,255,384 

26.3439 

8.8536 

.001440922 

2,180.27 

378,276.03 

G95 

483,025 

335,702,375 

26.3629 

8.8578 

.001438849 

2,183.41 

379,366.95 

696 

484,416 

337,153,536 

26.3818 

8.8621 

.001436782 

2,186.55 

380,459.44 

697 

485,809 

338,608,873 

20.4008 

8.8663 

.001434720 

2,189.69 

381,553.50 

G98 

487,204 

340,068,392 

26.4197 

8.8706 

.001432665 

2,192.83 

382,649.13 

699 

488,601 

341,532,099 

26.4386 

8.8748 

.001430615 

2,195.97 

383,746.33 

700 

490,000 

343,000,000 

26.4575 

8.8790 

.001428571 

2,199.11 

384,845.10 

701 

491,401 

344,472,101 

26.4764 

8.8833 

.001426534 

2,202.26 

385,945.44 

702 

492,804 

345,948,408 

26.4953 

8.8875 

.001424501 

2,205.40 

387,047.36 

703 

494,209 

347,428,927 

26.5141 

8.8917 

.001422475 

2,208.54 

388,150.84 

704 

495,616 

348,913,664 

26.5330 

8.8959 

.001420455 

2,211.68 

389,255.90 

705 

497,025 

350,402,625 

2G.5518 

8.9001 

.001418440 

2,214.82 

390,362.52 

706 

498,436 

351,895,816 

26.5707 

8.9043 

.001416431 

2,217.96 

391,470.72 

707 

499,849 

353,393,243 

26.5895 

8.9085 

.001414427 

2,221.11 

392,580.49 

708 

501,264 

354,894,912 

26.6083 

8.9127 

.001412429 

2,224.25 

393,691.82 

709 

502,681 

356,400,829 

26.6271 

8.9169 

.001410437 

2,227.39 

394,804.73 

710 

504,100 

357,911,000 

26.6458 

8.9211 

.001408451 

2,230.53 

395,919.21 

711 

505,521 

359,425,431 

26.6646 

8.9253 

.001406470 

2,233.67 

397,035.26 

712 

506,944 

360,944,128 

26.6833 

8.9295 

.001404494 

2,236.81 

398,152.89 

713 

508,369 

362,467,097 

2G.7021 

8.9337 

.001402525 

2,239.96 

399,272.08 

714 

509,796 

363,994,344 

26.7208 

8.9378 

.001400560 

2,243.10 

400,392.84 

715 

511,225 

365,525,875 

26.7395 

8.9420 

.001398601 

2,246.24 

401,515.18 

716 

512,656 

367,061,696 

26.7582 

8.9462 

.001396648 

2,249.38 

402,639.08 

717 

514,089 

368,601,813 

26.7769 

8.9503 

.001394700 

2,252.52 

403,764.56 

718 

515,524 

370,146,232 

26.7955 

8.9545 

.001392758 

2,255.66 

404,891.60 

719 

516,961 

371,694,959 

26.8142 

8.9587 

.001390821 

2,258.81 

406,020.22 

720 

518,400 

373,248,000 

26.8328 

8.9628 

.001388889 

2,261.95 

407,150.41 

721 

519,841 

374,805,361 

26.8514 

8.9670 

.001386963 

2,265.09 

408,282.17 

722 

521,284 

376,367,048 

26.8701 

8.9711 

.001385042 

2,268.23 

409,415.50 

723 

522,729 

377,933,067 

26.8887 

8.9752 

.001383126 

2,271.37 

410,550.40 

724 

524,176 

379,503,424 

26.9072 

8.9794 

.001381215 

2,274.51 

411,686.87 

725 

525,625 

381,078,125 

26.9258 

8.9835 

.001379310 

2,277.65 

412,824.91 

726 

527,076 

382,657,176 

26.9444 

8.9876 

.001377410 

2,280.80 

413,964.52 

727 

528,529 

384,240,583 

26.9629 

8.9918 

.001375516 

2,283.94 

415,105.71 

728 

529,984 

385,828,352 

26.9815 

8.9959 

.001373626  . 

2,287.08 

416,248.46 

729 

531,441 

387,420,489 

27.0000 

9.0000 

.001371742 

2,290.22 

417,392.79 

730 

532,900 

389,017,000 

27.0185 

9.0041 

.001369863 

2,293.36 

418,538.68 

731 

534,361 

390,617,891 

27.0370 

9.0082 

.001367989 

2,296.50 

419,686.15 

732 

535,824 

392,223,168 

27.0555 

9.0123 

.001366120 

2,299.65 

420,835.19 

733 

537,289 

393,832,837 

27.0740 

9.0164 

.001364256 

2,302.79 

421,985.79 

734 

538,756 

395,446,904 

27.0924 

9.0205 

.001362398 

2,305.93 

423,137.97 

735 

540,225 

397,065,375 

27.1109 

9.0246 

.001360544 

2,309.07 

424,291.72 

736 

54  J,  696 

398,688,256 

27.1293 

9.0287 

.001358696 

2,312.21 

425,447.04 

737 

543,169 

400,315,553 

27.1477 

9.0328 

.001356852 

2,315.35 

426,603.94 

738 

544,644 

401,947,272 

27.1662 

9.03G9 

.001355014 

2,318.50 

427,762.40 

739 

546,121 

403,583,419 

27.1846 

9.0410 

.001353180 

2,321.64 

428,922.43 

740 

547,600 

405,224,000 

27.2029 

9.0450 

.001351351 

2,324.78 

430,084.03 

741 

549,801 

406,869,021 

27.2213 

9.0491 

.001349528 

2,327.92 

431,247.21 

742 

550,564 

408,518,488 

27.2397 

9.0532 

.001347709 

2,331.06 

432,411.95 

743 

552,049 

410,172,407 

27.2580 

9.0572 

.001345895 

2,334.20 

433,578.27 

744 

553,536 

411,830,784 

27.2764 

9.0613 

.001344086 

2,337.34 

434,746.16 

745 

555,025 

413,493,625 

27.2947 

9.0654 

.001342282 

2,340.49 

435,915.62 

746 

556,516 

415,160,936 

27.3130 

9.0694 

.001340483 

2,343.63 

437,086.64 

747 

558,009 

416,832,723 

27.3313 

9.0735 

.001338688 

2,346.77 

438,259.24 

748 

559,504 

418,508,992 

27.3496 

9.0775 

.001336898 

2,349.91 

439,433.41 

2fi 


386 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circfum. 

Area 

749 

561,001 

420,189,749 

27.3679 

9.0816 

.001335113 

2,353.05 

440,609.16 

750 

562,500 

421,875,000 

27.3861 

9.0856 

.001333333 

2,356.19 

441,786.47 

751 

564,001 

423,564,751 

27.4044 

9.0896 

.001331558 

2,359.34 

442,965.35 

752 

565,504 

425,259,008 

27.4226 

9.0937 

.001329787 

2,362.48 

444,145.80 

753 

567,009 

426,957,777 

27.4408 

9.0977 

.001328021 

2,365.62 

445,327.83 

754 

568,516 

428,661,064 

27.4591 

9.1017 

.001326260 

2,368.76 

446,511.42 

755 

570,025 

430,368,875 

27.4773 

9.1057 

.001324503 

2,371.90 

447,696.59 

756 

571,536 

432,081,216 

27.4955 

9.1098 

.001322751 

2,375.04 

448,883.32 

757 

573,049 

433,798,093 

27.5136 

9.1138 

.001321004 

2,378.19 

450,071.63 

758 

574,564 

435,519,512 

27.5318 

9.1178 

.001319261 

2,381.33 

451,261.51 

759 

576,081 

437,245,479 

27.5500 

9.1218 

.001317523 

2,384.47 

452,452.96 

760 

577,600 

438,976,000 

27.5681 

9.1258 

.001315789 

2,387.61 

453,645.98 

761 

579,121 

410,711,081 

27.5862 

9.1298 

.001314060 

2,390.75 

454,840.57 

762 

580,644 

442,450,728 

27.6043 

9.1338 

.001312336 

2,393.89 

456,036.73 

763 

582,169 

444,194,917 

27.6225 

9.1378 

.001310616 

2,397.04 

457,234.46 

764 

583,696 

445,943,744 

27.6405 

9.1418 

.001308901 

2,400.18 

458,433.77 

765 

585,225 

447,697,125 

27.6586 

9.1458 

.001307190 

2,403.32 

459,634.64 

766 

586,756 

449,455,096 

27.6767 

9.1498 

.001305483 

2,406.46 

460,837.08 

767 
768 

588,289 
589,824 

451,217,663 
452,984,832 

27.6948 
27.7128 

9.1537 
9.1577 

.001303781 
.001302083 

2,409.60 
2,412.74 

462,041.10 
463,246.69 

769 

591,361 

454,756,609 

27.7308 

9.1617 

.001300390 

2,415.88 

464,453.84 

770 

-592,900 

456,533,000 

27.7489 

9.1657 

.001298701 

2,419.03 

465,662.57 

771 

594,441 

458,314,011 

27.7609 

9.1696 

.001297017 

2,422.17 

466,872.87 

772 

595,984 

460,099,648 

27.7849 

9.1736 

.001295337 

2,425.31 

468,084.74 

773 

597,529 

461,889,917 

27.8029 

9.1775 

.001293661 

2,428.45 

469,298.18 

774 

599,076 

463,684,824 

27.8209 

9.1815 

.001291990 

2,431.59 

470,513.19 

775 

600,625 

465,484,375 

27.8388 

9.185*5 

.001290323 

2,434.73 

471,729.77 

776 

602,176 

467,288,576 

27.8568 

9.1894 

.001288660 

2,437.88 

472,947.92 

777 

603,729 

469,097,433 

27.8747 

9.1933 

.001287001 

2,441.02 

474,167.65 

778 

605,284 

470,910,952 

27.8827 

9.1973 

.001285347 

2,444.16 

475,388.94 

779 

606,841 

472,729,139 

27.9106 

9.2012 

.001283697 

2,447.30 

476,611.81 

780 

608,400 

474,552,000 

27.9285 

9.2052 

.001282051 

2,450.44 

477,836.24 

781 

609,961 

476,379,541 

27.9464 

9.2091 

.001280410 

2,453.58 

479,062.25 

782 

611,524 

478,211,768 

27.9643 

9.2130 

.001278772 

2,456.73 

480,280.83 

783 

613,089 

480,048,687 

27  9821 

9.2170 

.001277139 

2,459.87 

481,518.97 

784 

614,656 

481,890,304 

28.0000 

9.2209 

.001275510 

2,463.01 

482,749.69 

785 

616,225 

483,736,625 

28.0179 

9.2248 

.001273885 

2,466.15 

483,081.98 

786 

617,796 

485,587,656 

28.0357 

9.2287 

.001272265 

2,469.29 

485,215.84 

787 

619,369 

487,443,403 

28.0535 

9.2326 

.001270648 

2,472.43 

486,451.28 

788 

620,944 

489,303,872 

28.0713 

9.2365 

.001269036 

2,475.58 

487,688.28 

789 

622,521 

491,169,069 

28.0891 

9.2404 

.001267427 

2,478.72 

488,926.85 

790 

624,100 

493,039,000 

28.1069 

9.2443 

.001265823 

2,481.86 

490,166.99 

791 

625,681 

494,913,671 

28.1247 

9.2482 

.001264223 

2,485.00 

491,408.71 

792 

627,264 

496,793,088 

28.1425 

9.2521 

.001262626 

2,488.14 

492,651.99 

793 

628,849 

498,677,257 

28.1603 

9.2560 

.001261034 

2,491.28 

493,896.85 

794 

630,436 

500,566,184 

28.1780 

9.2599 

.001259446 

2,494.42 

495,143.28 

795 

632,025 

502,459,875 

28.1957 

9.2638 

.001257862 

2,497.57 

496,391.27 

796 

633,616 

504,358,336 

28.2135 

9.2677 

.001256281 

2,500.71 

497,640.84 

797 

635,209 

506,261,573 

28.2312 

9.2716 

.001254705 

2,503.85 

498,891.98 

798 

636,804 

508,169,592 

28.2489 

9.2754 

.001253133 

2,506.99 

500,144.69 

799 

638,401 

510,082,399 

28.2666 

9.2793 

.001251364 

2,510.13 

501,398.97 

800 

640,000 

512,000,000 

28.2843 

9.2832 

.001250000 

2,513.27 

502,654.82 

801 

641,601 

513,922,401 

28.3019 

9.2870 

.001248439 

2,516.42 

503,912.25 

802 

643,204 

515,849,608 

28.3196 

9.2909 

.001246883 

2,519.56 

505,171.24 

803 

644,809 

517,781,627 

28.3373 

9.2948 

.001245330 

2,522.70 

506,431.80 

804 

646,416 

519,718,464 

28.3549 

9.2986 

.001243781 

2,525.84 

507,693.94 

805 

648,025 

521,660,125 

28.3725 

9.3025 

.001242236 

2,528.98 

508,957.64 

806 

649,636 

523,606,616 

28.3901 

9.3063 

.001240695 

2,532.12 

510,222.92 

807 

651,249 

525,557,943 

28.4077 

9.3102 

.001239157 

2,535.27 

511,489.77 

808 

652,864 

527,514,112 

28.4253 

9.3140 

.001237624 

2,538.41 

512,758.19 

809 

654,481 

529,475,129 

28.4429 

9.3179 

.001236094 

2,541.55 

514,028.18 

810 

656,100 

531,441,000 

28.4605 

9.3217 

.001234568 

2,544.69 

515,299.74 

811 

657,721 

533,411,731 

28.4781 

9.3255 

.001233046 

2,547.83 

516,572.87 

SQUARES,  CUBES,  ROOTS,  ETC. 


387 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Clrcum. 

Area 

812 

659,344 

535,387,328 

28.4956 

9.3294 

.001231527 

2,550.97 

517,847.57 

813 

660,969 

537,367,797 

28.5132 

9.3332 

.001230012 

2,554.11 

519,123.84 

814 

662,596 

539,353,144 

28.5307 

9.3370 

.001228501 

2,557.26 

520,401.68 

815 

r,t;i,225 

541,343,375 

28.5482 

9.3408 

.001226994 

2,560.40 

521,681.10 

816 

665,856 

543,338,496 

28.5657 

9.3447 

.001225490 

2,563.54 

522,962.08 

817 

667,489 

545,338,513 

28.5832 

9.3485 

.001223990 

2,566.68 

524,244.63 

818 

669,124 

547,343,432 

28.6007 

9.3523 

.001222494 

2,569.82 

525,528.76 

819 

670,761 

549,353,259 

28.6182 

9.3561 

.001221001 

2,572.96 

526,814.46 

820 

672,400 

551,368,000 

28.6356 

9.3599 

.001219512 

2,576.11 

528,101.73 

821 

674,041 

553,387,661 

28.6531 

9.3637 

.001218027 

2,579.25 

529,390.56 

822 

675,584 

555,412,248 

28.6705 

9.3675 

.001216545 

2,582.39 

530,680.97 

823 

677,329 

557,441,767 

28.6880 

9.3713 

.001215067 

2,585.53 

531,972.95 

824 

678,976 

559,476,224 

28.7054 

9.3751 

.001213592 

2,588.67 

533,266.50 

825 

680,625 

561,515,625 

28.7228 

9.3789 

.001212121 

2,591.81 

534,561.62 

826 

682!  276 

563,559,976 

28.7402 

9.3827 

.001210654 

2,594.96 

535,858.32 

827 

683,929 

565,609,283 

28.7576 

9.3865 

.001209190 

2,598.10 

537,156.58 

828 

685,584 

567,663,552 

28.7750 

93902 

.001207729 

2,601.24 

538,456.41 

829 

687,241 

569,722,789 

28.7924 

9.3940 

.001206273 

2,604.38 

539,757.82 

830 

688,900 

571,787,000 

28.8097 

9.3978 

.001204819 

2,607.52 

541,060.79 

831 

690,561 

573,856,191 

28.8271 

9.4016 

.001203369 

2,610.66 

542,365.34 

832 

692,224 

575,930,368 

28.8444 

9.4053 

.001201923 

2,613.81 

543,671.46 

833 

693,889 

578,009,537 

28.8617 

9.4091 

.001200480 

2,616.95 

544,979.15 

834 

695,556 

580,093,704 

28.8791 

9.4129 

.001199041 

2,620.09 

546,288.40 

835 

697,225 

582,182,875 

28.8964 

9.4166 

.001197605 

2,623.23 

547,599.23 

836 

698,896 

584,277,056 

28.9137 

9.4204 

.001196172 

2,626.37 

548,911.63 

837 

700,569 

586,376,253 

28.9310 

9.4241 

.001194743 

2,629.51 

550,225.61 

838 

702,244 

588,480,472 

28.9482 

9.4279 

.001193317 

2,632.65 

551,541.15 

839 

703,921 

590,589,719 

28.9655 

9.4316 

.001191895 

2,635.80 

552,858.26 

840 

705,600 

592,704,000 

28.9828 

9.4354 

.001190476 

2,638.94 

554,176.94 

841 

707,281 

594,823,321 

29.0000 

9.4391 

.001189061 

2,642.08 

555,497.20 

842 

708,964 

596,947,688 

29.0172 

9.4429 

.001187648 

2,645.22 

556,819.02 

843 

710,649 

599,077,107 

29.0345 

9.4466 

.001186240 

2,648.36 

558,142.42 

344 

712,336 

601,211,584 

29.0517 

9.4503 

.001184834 

2,651.50 

559,467.39 

845 

714,025 

603,351,125 

29.0689 

9.4541 

.001183432 

2,654.65 

560,793.92 

846 

715,716 

605,495,736 

29.0861 

9.4578 

.001182033 

2,657.79 

562,122.03 

847 

717,409 

607,645,423 

29.1033 

9.4615 

.001180638 

2,660.93 

563,451.71 

848 

719,104 

609,800,192 

29.1204 

9.4652 

.001179245 

2,664.07 

564,782.96 

849 

720,801 

611,960,049 

29.1376 

9.4690 

.001177856 

2,667.21 

566,115.78 

850 

722,500 

614,125,000 

29.1548 

9.4727 

.001176471 

2,670.35 

507,450.17 

851 

724,201 

616,295,051 

29.1719 

9.4764 

.001175088 

2,673.50 

508,786.14 

852 

725,904 

618,470,208 

29.1890 

9.4801 

.001173709 

2,676.64 

570,123.67 

853 

727,609 

620,650,477 

29.2062 

9.4838 

.001172333 

2,679.78 

571,462.77 

854 

729,316 

622,835,864 

29.2233 

9.4875 

.001170960 

2,682.92 

572,803.45 

855 

731,025 

625,026,375 

29.2404 

9.4912 

.001169591 

2,686.06 

574,145.69 

856 

732,736 

627,222,016 

29.2575 

9.4949 

.001168224 

2,689.20 

575,489.51 

857 

734,449 

629,422,793 

29.2746 

9.4986 

.001166861 

2,692.34 

576,834.90 

858 

736,164 

631,628,712 

29.2916 

9.5023 

.001165501 

2,695.49 

578,181.85 

859 

737,881 

633,839,779 

29.3087 

9.5060 

.001164144 

2,698.63 

579,530.38 

860 

739,600 

636,056,000 

29.3258 

9.5097 

.001162791 

2,701.77 

580,880.48 

861 

741,321 

638,277,381 

29.3428 

9.5135 

.001161440 

2,704.91 

582,232.15 

862 

743,044 

640,503,928 

29.3598 

9.5171 

.001160093 

2,708.05 

583,585.39 

863 

744,769 

642,735,647 

29.3769 

9.5207 

.001158749 

2,711.19 

584,940.20 

864 

746,496 

644,972,544 

29.3939 

9.5244 

.001157407 

2,714.34 

586,296.59 

865 

748,225 

647,214,625 

29.4109 

9.5281 

.001156069 

2,717.48 

587,654.54 

866 

749,956 

649,461,896 

29.4279 

9.5317 

.001154734 

2,720.62 

589,014.07 

867 

751,689 

651,714,363 

29.4449 

9.5354 

.001153403 

2,723.76 

590,375.16 

868 

753,424 

653,972,032 

29.4C18 

9.5391 

.001152074 

2,726.90 

591,737.83 

869 

755,161 

656.234,909 

29.4788 

9.5427 

.001150748 

2,730.04 

593,102.06 

870 

756,900 

658,503,000 

29.4958 

9.5464 

.001149425 

2,733.19 

594,467.87 

871 

758,641 

660,776,311 

29.5127 

9.5501 

.001148106 

2,736.33 

595,835.25 

872 

760,384 

663,054,848 

29.5296 

9.5537 

.001146789 

2,739.47 

597,204.20 

873 

762,129 

665,338,617 

29.5466 

9.5574 

.001145475 

2,742.61 

598,574.72 

874 

763,876 

667,627,624 

29.5635 

9.5610 

.001144165 

2,745.75 

599,946.81 

388 


MINE  GASES  AND  VENTILATION 


No. 

Square 

Cube 

Sq.  Boot 

Cu.  Boot 

Reciprocal 

_ 

Area 

875 

765,625 

'669,921,875 

29.5804 

9.5647 

.001142857 

2,748.89 

601,320.47 

876 

767,376 

672,221,376 

29.5973 

9.5683 

.001141553 

2,752.04 

602,695.70 

877 

769,129 

674,526,133 

29.6142 

9.5719 

.001140251 

2,755.18 

604,072.50 

878 

770,884 

676,836,152 

29.6311 

9.5756 

.001138952 

2,758.32 

605,450.88 

879 

772,641 

679,151,439 

29.6479 

9.5792 

.001137656 

2,761.46 

606,830.82 

880 

774,400 

681,472,000 

29.6648 

9.5828 

.001136364 

2,764.60 

608,212.34 

881 

776,161 

683,797.841 

29.6816 

9.5865 

.001135074 

2,767.74 

609,595.42 

882 

777,924 

686,128,968 

29.6985 

9.5901 

.001133787 

2,770.88 

610,980.08 

883 

779,689 

688,465,387 

29.7153 

9.5937 

.001132503 

2,774.03 

612,366.31 

884 

781,456 

690,807,104 

29.7321 

9.5973 

.001131222 

2,777.17 

613,754.11 

885 

783,225 

693,154,125 

29.7489 

9.6010 

.001129944 

2,780.31 

615,143.48 

886 

784,996 

695,506,456 

29.7658 

9.6046 

.001128668 

2,783.45 

616,534.42 

887 

786,769 

697,864,103 

29.7825 

9.6082 

.001127396 

2,786.59 

617,926.93 

888 

788,544 

700,227,072 

29.7993 

9.6118 

.001126126 

2,789.73 

619,321.01 

889 

790,321 

702,595,369 

29.8161 

9.6154 

.001124859 

2,792.88 

620,716.66 

890 

792,100 

704,969,000 

29.8329 

9.6190 

.001123596 

2,796.02 

622,113.89 

891 

793,881 

707,347,971 

29.8496 

9.6226 

.001122334 

2,799.16 

623,512.68 

892 

795,664 

707,932,288 

29.8664 

9.6262 

.001121076 

2,802.30 

624,913.04 

893 

797,449 

712,121,957 

29.8831 

9.6298 

.001119821 

2,805.44 

626,314.98 

894 

799,236 

714,516,984 

29.8998 

9.6334 

.001118568 

2,808.58 

627,718.49 

895 

801,025 

716,917,375 

29.9166 

9.6370 

.001117818 

2,811.73 

629,123.56 

896 

802,816 

719,323,136 

29.9333 

9.6406 

.001116071 

2,814.87 

630,530.21 

897 

804,609 

721,734,273 

29.9500 

9.6442 

.001114827 

2,818.01 

631,938.43 

898 

806,404 

724,150,792 

29.9666 

9.6477 

.001113586 

2,821.15 

633,348.22 

899 

808,201 

726,572,699 

29.9833 

9.6513 

.001112347 

2,824.29 

634,759.58 

900 

810,000 

729,000,000 

30.0000 

9.6549 

.001111111 

2,827.43 

636,172.51 

901 

811,801 

731,432,701 

30.0167 

9.6585 

.001109878 

2,830.58 

637,587.01 

902 

813,604 

733,870,808 

30.0333 

9.6620 

.001108647 

2,833.72 

639,003.09 

903 

815,409 

736,314,327 

30.0500 

9.6656 

.001107420 

2,836.86 

640,420.73 

904 

817,216 

738,763,264 

30.0666 

9.6692 

.001106195 

2,840.00 

641,839.95 

905 

819,025 

741,217,625 

30.0832 

9.6727 

.001104972 

2,843.14 

643,260.73 

906 

820,836 

743,677,416 

30.0998 

9.6763 

.001103753 

2,846.28 

644,683.09 

907 

822,649 

746,142,643 

30.1164 

9.6799 

.001102536 

2,849.42 

646,107.01 

908 

824,464 

748,613,312 

30.1330 

9.6834 

.001101322 

2,852.57 

647,532.51 

909 

826,281 

751,089,429 

30.1496 

9.6870 

.001100110 

2,855.71 

648,959.58 

910 

828,100 

753,571,000 

30.1662 

9.6905 

.001098901 

2,858.85 

650,388.22 

911 

829,921 

756,058,031 

30.1828 

9.6941 

.001091695 

2,861.99 

651,818.43 

912 

831,744 

758,550,825 

30.1993 

9.6976 

.001096491 

2,865.13 

653,250.21 

913 

833,569 

761,048,497 

30.2159 

9.7012 

.001095290 

2,868.27 

654,683.56 

914 

835,396 

763,551,944 

30.2324 

9.7047 

.001094092 

2,871.42 

656,118.48 

915 

837,225 

766,060,875 

80.2490 

9.7082 

.001092896 

2,874.56 

657,554.98 

916 

839,056 

768,575,296 

30.2655 

9.7118 

.001091703 

2,877.70 

658,993.04 

917 

840,889 

771,095,213 

30.2820 

9.7153 

.001090513 

2,880.84 

660,432.68 

918 

842,724 

773,620,632 

30.2985 

9.7188 

.001089325 

2,883.98 

661,873.88 

919 

844,561 

776,151,559 

30.3150 

9.7224 

.001088139 

2.887.12 

663,316.66 

920 

846,400 

778,688,000 

30.3315 

9.7259 

.001086957 

2,890.27 

664,761.01 

921 

848,241 

781,229,961 

30.3480 

9.7294 

.001085776 

2,893.41 

666,206.92 

922 

850,084 

783,777,448 

30.3645 

9.7329 

.001084599 

2,896.55 

667,654.41 

923 

851,929 

786,330,467 

30.3809 

9.7364 

.001083423 

2,899.69 

669,103.47 

924 

853,776 

788,889,024 

30.3974 

9.7400 

.001082251 

2,902.83 

670,554.10 

925 

855,625 

791,453,125 

30.4138 

9.7435 

.001081081 

2,905.97 

672,006.30 

926 

857,476 

794,022,776 

30.4302 

9.7470 

.001079914 

2,909.11 

673,460.08 

927 

859,329 

796,597,983 

30.4467 

9.7505 

.001078749 

2,912.26 

674,915.42 

928 

861,184 

799,178,752 

30.4631 

9.7540 

.001077586 

2,915.40 

676,372.33 

929 

863,041 

801,765,089 

30.4795 

9.7575 

.001076426 

2,918.54 

677,830.82 

930 

864,900 

804,357,000 

30.4959 

9.7610 

.001075269 

2,921.68 

679,290.87 

931 

866,761 

806,954,491 

30.5123 

9.7645 

.001074114 

2,924.82 

680,752.50 

932 

868,624 

809,557,568 

30.5287 

9.7680 

.001072961 

2,927.96 

682,215.69 

933 

870,489 

812,166,237 

30.5450 

9.7715 

.001071811 

2,931.11 

683,680.46 

934 

872,356 

814,780,504 

30.5614 

9.7750 

.001070664 

2,934.25 

685,146.80 

935 

874,225 

817,400,375 

30.5778 

9.7785 

.001069519 

2,937.39 

686,614.71 

936 

876,096 

820,025,856 

30.5941 

9.7829 

.001068376 

2,940.53 

688,084.19 

937 

877,969 

822,656,953 

30.6105 

9.7854 

.001067236 

2,943.67 

689,555.24 

SQUARES,  CUBES,  ROOTS,  ETC. 


389 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Clrcom. 

Area 

938 

879,844 

825,293,672 

30.6268 

9.7889 

.001066098 

2,946.81 

691,027.86 

939 

881,721 

827,936,019 

30.6431 

9.7924 

.001064963 

2,949.96 

692,502.05 

940 

883,600 

830,584,000 

30.6594 

9.7959 

.001063830 

2,953.10 

693,977.82 

941 

885,481 

833,237,621 

30.6757 

9.7993 

.001062699 

2,956.24 

695,455.15 

942 

887,364 

835,896,888 

30.6920 

9.8028 

.001061571 

2,959.38 

696,934.06 

943 

889,249 

838,561,807 

30.7083 

9.8063 

.001060445 

2,962.52 

698,414.53 

944 

891,136 

841,232,384 

30.7246 

9.8097 

.001059322 

2,965.66 

699,896.58 

945 

893,025 

843,908,625 

30.7409 

9.8132 

.001058201 

2,968.81 

701,380.19 

946 

894,916 

846,590,536 

30.7571 

9.8167 

.001057082 

2,971.95 

702,865.38 

947 

896,808 

849,278,128 

30.7734 

9.8201 

.001055966 

2,975.09 

704,352.14 

948 

8US.704 

851,971,392 

30.7896 

9.8236 

.001054852 

2,978.23 

705,840.47 

949 

900,601 

854,670,349 

30.8058 

9.8270 

.001053741 

2,981.37 

707,330.37 

950 

902,500 

857,375,000 

30.8221 

9.8305 

.001052632 

2,984.51 

708,821.84 

951 

904,401 

860,085,351 

:;o.s:;s;; 

9.8339 

.001051525 

2,987.65 

710,314.88 

952 

906,304 

862,801,408 

30.8545 

9.8374 

.001050420 

2,990.80 

711,809.50 

953 

908,209 

865,523,177 

30.8707 

9.8408 

.001049318 

2,993.94 

713,305.68 

954 

910,116 

868,250,664 

30.8869 

9.8443 

.001048218 

2,997.08 

714,803.43 

955 

912,025 

870,983,875 

30.9031 

9.8477 

.001047120 

3,000.22 

716,302.76 

956 

913,936 

873,722,816 

30.9192 

9.8511 

.001046025 

3,003.36 

717,803.66 

957 

915,849 

876,467,493 

30.9354 

9.8546 

.001044932 

3,006.50 

719,306.12 

958 

917,764 

879,217,912 

30.9516 

9.8580 

.001043841 

3,009.65 

720,810.16 

959 

919,681 

881,974,079 

30.9677 

9.8614 

.001042753 

3,012.79 

722,315.77 

960 

921,600 

884,736,000 

30.9839 

9.8648 

.001041667 

3,015.93 

723,822.95 

961 

923,521 

887,503,681 

31.0000 

9.8683 

.001040583 

3,019.07 

725,331.70 

962 

925,444 

890,277,128 

31.0161 

9.8717 

.001039501 

3,022.21 

726,842.02 

963 

927,369 

893,056,347 

31.0322 

9.8751 

.001038422 

3,025.35 

728,353.91 

964 

929,296 

895,841,344 

31.0483 

9.8785 

.001037344 

3,028.50 

729,867.37 

965 

931,225 

898,632,125 

31.0644 

9.8819 

.001036269 

3,031.64 

731,382.40 

966 

933,156 

901,428,696 

31.0805 

9.8854 

.001035197 

3,034.78 

732,899.01 

967 

935,089 

904,231,063 

31.0966 

9.8888 

.001034126 

3,037.92 

734,417.18 

968 

937,024 

907,039,232 

31.1127 

9.8922 

.001033058 

3,041.06 

735,936.93 

969 

938,961 

909,853,209 

31.1288 

9.8956 

.001031992 

3,044.20 

737,458.24 

970 

940,900 

912,673,000 

31.1448 

9.8990 

.001030928 

3,047.34 

738,981.13 

971 

942,841 

915,498,611 

31.1609 

9.9024 

.001029866 

3,050.49 

740,505.59 

972 

944,784 

918,330,048 

31.1769 

9.9058 

.001028807 

3,053.63 

742,031.62 

973 

946,729 

921,167,317 

31.1929 

9.9092 

.001027749 

3,056.77 

743,559.22 

974 

948,676 

924,010,424 

31.2090 

9.9126 

.001026694 

3,059.91 

745,088.39 

975 

950,625 

926,859,375 

31.2250 

9.9160 

.001025641 

3,063.05 

746,619.13 

976 

952,576 

929,714,176 

31.2410 

9.9194 

.001024590 

3,066.19 

748,151.44 

977 

954,529 

932,574,833 

31.2570 

9.9228 

.001023541 

3,069.34 

749,685.32 

978 

956,484 

935,441,352 

31.2730 

9.9261 

.001022495 

3,072.48 

751,220.78 

979 

958,441 

938,313,739 

31.2890 

9.9295 

.001021450 

3,075.62 

752,757.80 

980 

960,400 

941,192,000 

31.3050 

9.9329 

.001020408 

3,078.76 

754,296.40 

981 

962,361 

944,076,141 

31.3209 

9.9363 

.001019168 

3,081.90 

755,836.56 

982 

964,324 

946,966,168 

31.3369 

9.9396 

.001018330 

3,085.04 

757,378.30 

983 

966,289 

949.862,087 

31.3528 

9.9430 

.001017294 

3,088.19 

758,921.61 

984 

968,256 

952,763,904 

31.3698 

9.9464 

.001016260 

3,091.33 

760,466.48 

985 

970,225 

955,671,625 

31.3847 

9.9497 

.001015228 

3,094.47 

762,012.93 

986 

972,196 

958,585,256 

31.4006 

9.9531 

.001014199 

3,097.61 

763,560.95 

987 

974,169 

961,504,803 

31.4166 

9.9565 

.001013171 

3,100.75 

765,110.54 

988 

976,144 

964,430,272 

31.4325 

9.9598 

.001012146 

3,103.89 

766,661.70 

989 

978,121 

967,361,669 

31.4484 

9.9632 

.001011122 

3,107.04 

768,214.44 

990 

980,100 

970,299,000 

31.4643 

9.9666 

.001010101 

3,110.18 

769,768.74 

991 

982,081 

973,242,271 

31.4802 

9.9699 

.001009082 

3,113.32 

771,324.61 

992 

984,064 

976,191,488 

31.4960 

9.9733 

.001008065 

3,116.46 

772,882.06 

993 

986,049 

979,146,657 

31.5119 

9.9766 

.001007049 

3,119.60 

774,441.07 

994 

988,036 

982,107,784 

31.5278 

9.9800 

.001006036 

3,122.74 

776,001.66 

995 

990,025 

985,074,875 

31.5436 

9.9833 

.001005025 

3,125.88 

777,563.82 

996 

992,016 

988,047,936 

31.5595 

9.9866 

.001004016 

3,129.03 

779,127.54 

997 

994,009 

991,026,973 

31.5753 

9.9900 

.001003009 

3,132.17 

780,692.84 

998 

996,004 

994,011,992 

31.5911 

9.9933 

.001002004 

3,135.31 

782,259.71 

999 

998,001 

997,002,999 

31.6070 

9.9967 

.001001001 

3,138.45 

783,828.15 

1000 

1,000,000 

1,000,000,000 

31.6228 

10.0000 

.001000000 

3,141.59 

785,398.16 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 


391 


392 


MINE  GASES  AND  VENTILATION 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES  FROM  1-64  to  100 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

A 

.0491 

.0002 

6 

18.8496 

28.2744 

13} 

41.2335 

135.297 

JL 

.0982 

.0008 

6} 

19.2423 

29.4648 

13} 

41.6262 

137.887 

A 

.1963 

.0031 

4 

19.6350 

30.6797 

181 

42.0189 

140.501 

i 

.3927 

.0123 

6f 

20.0277 

31.9191 

m 

42.4116 

143.139 

JL 

.5890 

.0276 

6* 

20.4204 

33.1831 

13£ 

42.8043 

145.802 

1 

.7854 

.0491 

6| 

20.8131 

31.4717 

13} 

43.1970 

148.490 

JL 

.9817 

.0767 

6* 

21.2058 

35.7848 

13| 

43.5897 

151.202 

i 

1.1781 

.1104 

61 

21.5985 

37.1224 

14 

43.9824 

153.938 

™ 

1.3744 

.1503 

7 

21.9912 

38.4846 

14} 

44.3751 

156.700 

i 

1.5708 

.1963 

7} 

22.3839 

39.8713 

14} 

44.7678 

159.485 

A 

1.7671 

.2485 

7} 

22.7766 

41.2826 

14f 

45.1605 

162.296 

i 

1.9635 

.3068 

7i 

23.1693 

42.7184 

14| 

45.5532 

165.130 

A 

2.1598 

.3712 

74 

23.5620 

44.1787 

14| 

45.9459 

167.990 

2.3562 

.4418 

71 

23.9547 

45.6636 

14| 

46.3386 

170.874 

ii 

2.5525 

.5185 

7* 

24.3474 

47.1731 

141 

46.7313 

173.782 

i 

2.7489 

.6013 

7| 

24.7401 

48.7071 

15 

47.1240 

176.715 

16 

2.9452 

.6903 

8 

25.1328 

50.2656 

15} 

47.5167 

179.673 

1 

3.1416 

.7854 

8* 

25.5255 

51.8487 

15j 

47.9094 

182.655 

If 

3.5343 

.9940 

3 

25.9182 

53.4563 

•  15| 

48.3021 

185.661 

1} 

3.9270 

1.2272 

8* 

26,3109 

55.0884 

15* 

48.C948 

188.692 

if 

4.3197 

1.4849 

8* 

26.7036 

56.7451 

15| 

49.0875 

•191.748 

l{ 

4.7124 

1.7671 

81 

27.0963 

58.4264 

15} 

49.4802 

194.828 

1* 

5.1051 

2.0739 

82 

27.4890 

60.1322 

151 

49.8729 

197.933 

1} 

5.4978 

2.4053 

81 

27.8817 

61.8625 

16 

50.2056 

201.062 

1* 

5.8905 

2.7612 

9 

28.2744 

63.6174 

16} 

50.6583 

204.216 

2 

6.2832 

3.1416 

9j 

28.6671 

65.3968 

16} 

51.0510 

207.395 

2| 

6.6759 

3.5466 

9? 

29.0598 

67.2008 

16f 

51.4437 

210.598 

2} 

7.0686 

3.9761 

9i 

29.4525 

69.0293 

16£ 

51.8364 

213.825 

2* 

7.4613 

4.4301 

9i 

29.8452 

70.8823 

16| 

52.2291 

217.077 

3 

7.8540 

4.9087 

91 

30.2379 

72.7599 

16} 

52.6218 

220.354 

2* 

8.2467 

5.4119 

9i 

30.6306 

74.6621 

161 

53.0145 

223.655 

2* 

8.6394 

5.9396 

9* 

31.0233 

76.589 

17 

53.4072 

226.981 

2* 

9.0321 

6.4918 

10 

31.4160 

78.540 

17* 

53.7999 

230.331 

3 

9.4248 

7.0686 

10* 

31.8087 

80.516 

17} 

54.1926 

233.706 

1 

3| 

9.8175 
10.2102 
10.6029 

7.6699 
8.2058 
8.9462 

10}. 

a 

32.2014 
32.5941 

32.9868 

82.516 
84.541 
86.590 

1 

54.5853 
54.9780 
55.3707 

237.105 
240.529 
243.977 

9 

10.9956 

9.6211 

10| 

33.3795 

88.664 

17} 

55.7634 

247.450 

3| 

11.3883 

10.3206 

101 

33.7722 

90.763 

171 

56.1561 

250.948 

3* 

11.7810 

11.0447 

loj 

34.1649 

92.886 

18 

56.5488 

254.470 

3* 

12.1737 

11.7933 

11 

34.5576 

95.033 

18* 

56.9415 

258.016 

4 

12.5664 

12.5664 

1H 

34.9503 

97.205 

18} 

57.3342 

261.587 

4« 

12.9591 

13.3641 

111 

35.3430 

99.402 

18| 

57.7269 

265.183 

4^ 

13.3518 

14.1863 

Hf 

35.7357 

101.623 

18* 

58.1196 

268.803 

4* 

13.7445 

15.0330 

11* 

36.1284 

103.869 

181 

58.5123 

272.448 

4 

14.1372 

15.9043 

HI 

36.5211 

106.139 

18} 

58.9050 

276.117 

4| 

14.5299 

16.8002 

11} 

36.9138 

108.434 

181 

59.2977 

279.811 

4| 

14.9226 

17.7206 

111 

37.3065 

110.754 

19 

59.6904 

283.529 

4f 

15.3153 

18.6555 

12 

37.6992 

113.098 

19} 

60.0831 

287.272 

5 

15.7080 

19.6350 

12* 

38.0919 

115.466 

19} 

60.4758 

291.040 

5r 

16.1007 

20.6290 

12! 

38.4846 

117.859 

19£ 

60.8685 

294.832 

5} 

16.4934 

21.6476 

12f 

38.8773 

120.277 

19>- 

61.2612 

298-648 

5 

16.8861 

22.6907 

12* 

39.2700 

122.719 

19| 

61.6539 

302.489 

b, 

17.2788 

23.7583 

12f 

39.6627 

125.185 

19} 

62.0466 

306.355 

5i 

17.6715 

24.8505 

40.0554 

127.677 

191 

62.4393 

310.245 

5; 

18.0642 

25.9673 

12- 

40.4481 

130.192 

20 

62.8320 

314.160 

5* 

18.4569 

27.1086 

13 

40.8408 

132.733 

20} 

63.2247 

318.099 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES       393 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

20} 

63.6174 

322.063 

28* 

88.3575 

621.264 

36 

113.098 

1,017.878 

201 

64.0101 

326.051 

28; 

88.7502 

626.798 

3Q1 

113.490 

1,024.960 

20* 

64.4028 

330.064 

28j 

89.1429 

632.357 

36- 

113.883 

1,032.065 

20| 

64.7955 

334.102 

28j- 

89.5356 

637.941 

361 

114.276 

1,039.195 

20* 

65.1882 

338.164 

28  J 

89.9283 

013.549 

36* 

114.668 

1,046.349 

20* 

65.5809 

342.250 

28* 

90.3210 

649.182 

36| 

115.061 

1,053.528 

21 

65.9736 

346.361 

28* 

90.7137 

654.840 

36* 

115.454 

1,060.732 

66.3663 

350.497 

29 

91.1064 

660.521 

36* 

115.846 

1,067.960 

21- 

66.7590 

354.657 

29} 

91.4991 

6G6.228 

37 

116.239 

1,075.213 

21  1 

67.1517 

358.842 

29! 

91.8918 

671.959 

37} 

116.632 

1,082.490 

21* 

67.5444 

363.051 

291 

92.2845 

677.714 

37! 

117.025 

1,089.792 

67.9371 

367.285 

29* 

92.6772 

683.494 

37f 

117.417 

1,097.118 

21* 

68.3298 

371.543 

29| 

93.0699 

689.299 

37* 

117.810 

1,104.469 

21* 

68.7225 

375.826 

29* 

93.4626 

695.128 

118.203 

1,111.844 

22 

69.1152 

380.134 

29* 

93.8553 

700.982 

37| 

118.595 

1,119.244 

T>\ 

69.5079 

384.4G6 

30 

94.2480 

706.860 

37* 

118.988 

1,126.669 

22| 

69.9006 

388.822 

30} 

94.6407 

712.763 

38 

119.381 

1,134.118 

22| 

70.2933 

393.203 

30} 

95.0334 

718.690 

38i 

119.773 

1,141.591 

70.68GO 

397.609 

30| 

95.4261 

724.642 

38! 

120.1G6 

1,149.089 

22  1 

71.0787 

402.038 

30* 

95.8188 

730.618 

381 

120.559 

1,156.612 

22* 

71.4714 

406.494 

30| 

96.2115 

736.619 

38* 

120.952 

1,164.159 

22* 

71.8641 

410.973 

30* 

96.6042 

742.645 

38| 

121.344 

1,171.731 

23 

72.2568 

415.477 

30* 

96.9969 

748.695 

38* 

121.737 

1,179.327 

23} 

72.6495 

•420.004 

31 

97.3896 

754.769 

38* 

122.130 

1,186.948 

23! 

73.0422 

424.558 

31} 

97.7823 

760.869 

39 

122.522 

1,194.593 

23| 

73.4349 

429.135 

31} 

98.1750 

766.992 

39} 

122.915 

1,202.263 

23* 

73.8276 

433.737 

311 

98.5677 

773.140 

39! 

123.308 

1,209.958 

23| 

74.2203 

438.364 

31* 

98.9604 

779.313 

391 

123.700 

1,217.677 

23* 

74.6130 

443.015 

31  1 

99.3531 

785.510 

39* 

124.093 

1,225.420 

23* 

75.0057 

447.690 

31* 

99.7458 

791.732 

89* 

124.486 

1,233.188 

24 

75.3984 

452.390 

31* 

100.1385 

797.979 

39* 

124.879 

1,240.981 

241 

75.7911 

457.115 

32 

100.5312 

804.250 

39* 

125.271 

1,248.798 

76.1838 

461.864 

32} 

100.9239 

810.545 

40 

125.664 

1,256.640 

24| 
24* 

76.5765 
76.9692 

466.638 
471.436 

32} 
32| 

101.3166 
101.7093 

816.865 
823.210 

40i 
40} 

126.057 
126.449 

1,264.510 
1,272.400 

24f 

77.3619 

476.259 

32* 

102.1020 

829.579 

401 

126.842 

1,280.310 

24* 

77.7546 

481.107 

32| 

102.4947 

835.972 

40* 

127.235 

1,288.250 

24* 

78.1473 

485.979 

32* 

102.8874 

842.391 

40| 

127.627 

1,296.220 

25 

78.5400 

490.875 

32* 

103.280 

848.833 

40* 

128.020 

1,304.210 

25} 

78.9327 

495.796 

33 

103.673 

855.301 

40* 

128.413 

1,312.220 

25| 

79.3254 

500.742 

33} 

104.065 

861.792 

41 

128.806 

1,320.260 

25| 

79.7181 

505.712 

33} 

104.458 

8G8.309 

41* 

129.198 

1,328.320 

25* 

80.1108 

510.706 

33| 

104.851 

874.850 

41-1 

129.591 

1,336.410 

25| 

80.5035 

515.726 

33* 

105.244 

881.415 

41  * 

129.984 

1,344.520 

25* 

80.8962 

520.769 

331 

105.636 

888.005 

41* 

130.376 

1,352.660 

25* 

81.2889 

525.838 

33* 

106.029 

894.620 

41* 

130.769 

1,360.820 

26 

81.6816 

530.930 

33* 

106.422 

901.259 

41* 

131.162 

1,369.000 

2Gi 

82.0743 

536.048 

34 

106.814 

907.922 

41* 

131.554 

1,377.210 

26} 

82.4670 

541.190 

34} 

107.207 

914.611 

42 

131.947 

1J385.450 

2C| 

82.8597 

546.356 

34} 

107.600 

921.323 

42} 

132.340 

1,393.700 

26* 

83.2524 

551.547 

3-1* 

107.992 

928.061 

42! 

132.733 

1,401.990 

26| 

83.6451 

556.763 

34* 

108.385 

934.822 

421 

133.125 

1,410.300 

26* 

84.0378 

5G2.003 

34| 

108.778 

941.609 

42* 

133.518 

1,418.630 

26* 

84.4305 

567.2G7 

34* 

109.171 

948.420 

42* 

133.911 

1,426.990 

27 

84.8232 

572.557 

34* 

109.563 

955.255 

42* 

134.303 

1,435.370 

27i 

85.2159 

577.870 

35 

109.956 

962.115 

42* 

134.696 

1,443.770 

27} 

85.6086 

583.209 

35| 

110.349 

969.000 

43 

135.089 

1,452.200 

27f 

86.0013 

588.571 

110.741 

975.909 

431 

135.481 

1,460.660 

27* 

86.3940 

593.959 

35| 

111.134 

982.842 

135.874 

1,469.140 

27f 

86.7867 

599.371 

35* 

111.527 

989.800 

431 

136.267 

1,477.640 

27* 

87.1794 

604.807 

35* 

111.919 

996.783 

43* 

136.660 

1,486.170 

27* 

87.5721 

610.208 

35* 

112.312 

1,003.790 

43* 

137.052 

1,494.730 

28 

87.9648 

615.754 

35* 

112.705 

1,010.822 

43* 

137.445 

1,503.300 

394 


MINE  GASES  AND  VENTILATION 


Diam. 

Circum 

Area 

Diam 

Circum 

Area 

Diam 

Circum 

Area 

43} 

137.838 

1,511.910 

511 

162.578 

2,103.35 

59f 

187.318 

2,792.21 

44 

138.230 

1,520.530 

51} 

162.970 

2,113.52 

59? 

187.711 

2,803.93 

44i 

138.623 

1,529.190 

52 

163.363 

2,123.72 

591 

188.103 

2,815.67 

44} 

139.016 

1,537.860 

52} 

163.756 

2,133.94 

60 

188.496 

2,827.44 

44f 

139.408 

1,546.56 

52} 

164.149 

2,144.19 

60} 

188.889 

2,839.23 

44} 

139.801 

1,555.29 

52| 

164.541 

2,154.46 

60} 

189.281 

2,851.05 

44| 

140.194 

1,564.04 

52i 

164.934 

2,164.76 

60| 

189.674 

2,862.89 

44? 

140.587 

1,572.81 

52* 

165.327 

2,175.08 

60} 

190.067 

2,874.76 

44} 

140.979 

1,581.61 

52? 

165.719 

2,185.42 

60| 

190.459 

2,886.65 

45 

141.372 

1,590.43 

521 

166.112 

2,195.79 

60? 

190.852 

2,898.57 

45i 

141.7G5 

1,599.28 

53 

166.505 

2,206.19 

601 

191.245 

2,910.51 

45| 

142.157 

1,608.16 

53} 

166.897 

2,216.61 

61 

191.638 

2,922.47 

45| 

142.550 

1,617.05 

53* 

167.290 

2,227.05 

61} 

192.030 

2,934.46 

45} 

142.943 

1,625.97 

53f 

167.683 

2,237.52 

6l| 

192.423 

2,946.48 

45| 

143.335 

1,634.92 

53} 

168.076 

2,248.01 

61J 

192.816 

2,958.52 

45| 

143.728 

1,643.89 

168.468 

2,258.53 

61} 

193.208 

2,970.58 

45} 

144.121 

1,652.89 

53? 

168.861 

2,269.07 

61| 

193.601 

2,982.67 

46 

144.514 

1,661.91 

53} 

169.254 

2,279.64 

61? 

193.994 

2,994.78 

46} 

144.906 

1,670.95 

54 

169.646 

2,290.23 

611 

194.386 

3,006.92 

46} 

145.299 

1,680.02 

54} 

170.039 

2,300.84 

62 

194.779 

3,019.08 

46f 

145.692 

1,689.11 

54} 

170.432 

2,311.48 

62} 

195.172 

8,031.26 

46} 

146.084 

1,698.23 

54| 

170.824 

2,322.15 

62} 

195.565 

3,043.47 

46| 

146.477 

1,707.37 

54} 

171.217 

2,332.83 

62f 

195.957 

3,055.71 

46| 

146.870 

1,716.54 

54| 

171.610 

2,343.55 

62} 

196.350 

3,067.97 

46} 

147.262 

1,725.73 

54? 

172.003 

2,354.29 

62| 

196.743 

3,080.25 

47 

147.655 

1,734.95 

54} 

172.395 

2,365.05 

62? 

197.135 

3,092.56 

47} 

148.048 

1,744.19 

55 

172.788 

2,375.83 

621 

197.528 

3,104.89 

47J 

148.441 

1,753.45 

55} 

173.181 

2,386.65 

63 

197.921 

3,117.25 

47f 

148.833 

1,762.74 

55} 

173.573 

2,397.48 

63} 

198.313 

3,129.64 

47| 

149.226 

1,772.06 

55f 

173.966 

2,408.34 

63} 

198.706 

3,142.04 

47| 

149.619 

1,781.40 

55} 

174.359 

2,419.23 

63f 

199.099 

3.154.47 

47? 

150.011 

1,790.70 

55| 

174.751 

2,430.14 

63} 

199.492 

3,166.93 

47i 

150.404 

1,800.15 

55? 

175.144 

2,441.07 

63| 

199.884 

3,179.41 

48 

150.797 

1,8C9.56 

55^ 

175.537 

2,452.03 

63? 

200.277 

3.191.91 

48} 

151.189 

1,819.00 

56 

175.930 

2,463.01 

63} 

200.670 

3,204.44 

48} 

151.582 

1,828.46 

56} 

176.322 

2,474.02 

64 

201.062 

3,217.00 

48f 

151.975 

1,837.95 

56} 

176.715 

2,485.05 

64} 

201.455 

3,229.58 

48} 

152.368 

1,847.46 

56f 

177.108 

2,496.11 

64* 

201.848 

3,242.18 

48| 

152.760 

1,856.99 

56} 

177.500 

2,507.19 

64| 

202.240 

3,254.81 

481 

153.153 

1,866.55 

177.893 

2,518.30 

64| 

202.633 

3,267.46 

48| 

153.546 

1,876.14 

56? 

178.286 

2,529.43 

64| 

203.026 

3,280.14 

49 

153.938 

1,885.75 

561 

178.678 

2,540.58 

64? 

203.419 

3,292.84 

49} 

154.331 

1,895.38 

57 

179.071 

2,551.76 

64} 

203.811 

3,305.56 

49| 

154.724 

1,905.04 

.57} 

179.464 

2,562.97 

65 

204.204 

3,318.31 

49f 

155.116 

1,914.72 

57} 

179.857 

2,574.20 

65^ 

204.597 

3,331.09 

49} 

155.509 

1,924.43 

57| 

180.249 

2,585.45 

65J 

204.989 

3,343.89 

49| 

155.902 

1,934.16 

57} 

180.642 

2,596.73 

65f 

205.382 

3,356.71 

49? 

156.295 

1,943.91 

57$ 

181.035 

2,608.03 

65} 

205.775 

3.369.56 

49i 

156.687 

1,953.69 

57* 

181.427 

2,619.36 

65| 

206.167 

3;382.44 

50 

157.080 

1,963.50 

571 

181.820 

"630.71 

65? 

206.560 

3,395.33 

50} 

157.473 

1,973.33 

58 

182.213 

2,63.09 

65} 

206  953 

3,408.26 

50| 

157.865 

1,983.18 

58- 

182.605 

2,653.49 

66 

207.346 

3,421.20 

50| 

158.258 

1,993.06 

58* 

182.998 

2,664.91 

66^ 

207.738 

3,434.17 

50} 

158.651 

2,002.97 

58| 

183.391 

2,676.36 

66| 

208.131 

3,447.17 

50| 

159.043 

2,012.89 

58j 

183.784 

2,687.84 

66| 

208.524 

3,460.19 

50| 

159.436 

2,022.85 

58| 

184.176 

2,699.33 

66} 

208.916 

3,473.24 

50} 

159.829 

2,032.82 

58? 

184.569 

2,710.86 

66f 

209.309 

3,486.30 

51 

160.222 

2,042.83 

581 

184.962 

2,722.41 

66? 

209.702 

3,499.40 

61* 

160.614 

2,052.85 

59 

185.354 

2,733.98 

66} 

210.094 

3,512.52 

5l| 

161.007 

2,062.90 

59} 

185.747 

2,745.57 

67 

210.487 

3,525.66 

51f 

161.400 

2,072.98 

59| 

186.140 

2,757.20 

67} 

210.880 

3,538.83 

51} 

161.792 

2,083.08 

59J 

186.532 

2,768.84 

67} 

211.273 

3,552.02 

51* 

162.185 

2,093.20 

59} 

186.925 

2,780.51 

671 

211.665 

3,565.24 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES       395 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

67* 

212.058 

3,578.48 

75| 

236.798 

4,462.16 

83} 

261.538 

5,443.26 

67J 

212.451 

3,591.74 

237.191 

4,476.98 

83} 

261.931 

5,459.62 

67* 

212.843 

3,605.04 

75| 

237.583 

4,491.81 

83L 

262.324 

6,476.01 

67} 

213.236 

3,618.35 

75* 

237.976 

4,506.67 

83* 

262i716 

5,492.41 

68 

213.629 

3,631.69 

75} 

238.369 

4,521.56 

83* 

263.109 

5,508.84 

68i 

214.021 

3,645.05 

76 

238.762 

4,536.47 

83} 

263.502 

6,525.30 

68i 

214.414 

3,658.44 

76i 

239.154 

4,551.41 

84 

263894 

5,541.78 

68* 

214.807 

3,671.86 

76} 

239.547 

4,566.36 

84} 

264.287 

5,558.29 

215.200 

3,685.29 

76f 

239.940 

4,581.35 

84} 

264.680 

6,574.82 

68| 

215.592 

3,698.76 

76* 

240.332 

4,596.36 

84| 

265.072 

5,591.37 

68* 

215.985 

3,712.24 

76  J 

240.725 

4,611.39 

84* 

265.465 

5,607.95 

68} 

216.378 

3,725.75 

76* 

241.118 

4,626.45 

84* 

265.858 

5,624.56 

89 

216.770 

3,739.29 

76} 

241.510 

4,641.53 

84* 

266.251 

5,641.18 

217.163 

3,752.85 

77 

241.903 

4,656.64 

84} 

266.643 

5,657.84 

69f 

217.556 

3,766.43 

77} 

242.296 

4,671.77 

8? 

267.036 

5,674.51 

69* 

217.948 

3,780.04 

77} 

242.689 

4,686.92 

267.429 

5,691.22 

69* 

218.341 

3,793.68 

771 

243.081 

4,702.10 

1} 

267.821 

5,707.94 

69| 

218.734 

3,807.34 

77* 

2-13.474 

4,717.31 

85| 

268.214 

5,724.69 

69* 

219.127 

3,821.02 

77| 

243.867 

4,732.54 

85* 

268.607 

5,741.47 

69} 

219.519 

3,834.73 

77| 

244.259 

4,747.79 

85* 

268.999 

6,758.27 

70 

219.912 

3,848.46 

77} 

244.652 

4,763.07 

85* 

269.392 

5,775.10 

70i 

220.305 

3,862.22 

78 

245.045 

4,778.37 

85} 

269.785 

5,791.94 

70* 

220.697 

3,876.00 

7ft  t 

245.437 

4,793.70 

86 

270.178 

5,808.82 

70| 

221.090 

3,889.80 

78} 

245.830 

4,809.05 

863 

270.570 

5,825.72 

70* 

221.483 

3.903.C3 

78J 

246.223 

4,824.43 

86; 

270.963 

5,842.64 

70  1 

221.875 

3,917.49 

246.616 

4,839.83 

86 

271.356 

5,859.59 

70* 

222.268 

3,931.37 

78>- 

247.008 

4,855.26 

86, 

271.748 

5,876.56 

70} 

222.661 

3,945.27 

78* 

247.401 

4,870.71 

86 

272.141 

5,893.55 

71 

223.054 

3,959.20 

78} 

247.794 

4,886.18 

86. 

272.534 

5,910.58 

71} 

223.416 

3,973.15 

79 

248.186 

4,901.68 

86} 

272.926 

5,927.62 

71} 

223.839 

3,987.13 

79} 

248.579 

4,917.21 

87 

273.319 

5,944.69 

71  1 

224.232 

4,001.13 

79} 

248.972 

4,932.75 

273.712 

5,961.79 

71* 

224.624 

4,015.16 

79J 

249.364 

4,948.33 

87} 

274.105 

5,978.91 

71* 

225.017 

4,029.21 

79* 

249.757 

4,963.92 

87| 

274.497 

5,996.05 

71* 

225.410 

4,043.29 

79| 

250.150 

4,979.55 

274.890 

6,013.22 

71} 

225.802 

4,057.39 

79* 

250.543 

4,995.19 

87| 

275.283 

6,030.41 

72 

226.195 

4,071.51 

79} 

250.935 

6,010.86 

87* 

275.675 

6,047.63 

72} 

226.588 

4,085.66 

80 

251.328 

5,026.56 

87} 

276.068 

6,064.87 

72^- 

226.981 

4,099.84 

80} 

251.721 

5,042.28 

88 

276.461 

6,082.14 

1! 

227.373 
227.766 

4,114.04 

4,128.26 

80| 

252.113 
252.506 

5,058.03 
5,073.79 

881 
88i 

276.853 
277.246 

6,099.43 
6,116.74 

72* 

228.159 

4,142.51 

80* 

252.899 

5,089.59 

88 

277.629 

6,134.08 

72* 

228.551 

4,156.78 

80| 

253.291 

5,105.41 

88, 

278.032 

6,151.45 

72} 

228.944 

4,171.08 

80* 

253.684 

5,121.25 

88 

278.424 

6,168.84 

73 

229.337 

4,185.40 

80} 

254.077 

5,137.12 

88: 

278.817 

6,186.25 

a 

229.729 
230.122 

4,199.74 
4,214.11 

81 
81} 

254.470 
254.862 

5,153.01 
6,168.93 

88} 
89 

279.210 
279.602 

6,203.69 
6,221.15 

73  1 

230.515 

4,228.51 

81- 

255.255 

5,184.87 

89^ 

279.995 

6,238.64 

73* 

230.908 

4,242.93 

fflf 

255.648 

5,200.83 

89; 

280.388 

6,256.15 

73| 

231.300 

4,257.37 

81* 

256.040 

5,216.82 

89 

280.780 

6,273.69 

73* 

231.693 

4,271.84 

81* 

256.433 

5,232.84 

89; 

281.173 

6,291.25 

73} 

232.086 

4,286.33 

81* 

256.826 

5,248.88 

89 

281.566 

6,308.84 

74 

232.478 

4,300.85 

81} 

257.218 

5,264.94 

893 

281.959 

6,326.45 

74} 

232.871 

4,315.39 

82 

257.611 

6,281.03 

89} 

282.351 

6,344.08 

74r 

233.264 

4,329.96 

82?i 

258.004 

5,297.14 

90 

282.744 

6.361.74 

74| 

233.656 

4,344.55 

82} 

258.397 

6,313.28 

90} 

283.137 

6,379.42 

74* 

234.049 

4,359.17 

82f 

258.789 

5,329.44 

90} 

283.529 

6,397.13 

741 

234.442 

4,373.81 

259.182 

5,345.63 

90| 

283.922 

6,414.86 

234.835 

4,388.47 

82| 

259.575 

5,361.84 

90* 

284.315 

6,432.62 

74} 

235.227 

4,403.16 

82* 

259.967 

5,378.08 

90* 

284.707 

6,450.40 

75 

235.620 

4,417.87 

82} 

260.360 

5,394.34 

90* 

285.100 

6,468.21 

75} 

236.013 

4,432.61 

83 

250.753 

6,410.62 

90} 

285.493 

6,486.04 

75} 

236.405 

4,447.38 

83} 

261.145 

5,426.93 

91 

285.886 

6,503.90 

396 


MINE  GASES  AND  VENTILATION 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

91} 

286.278 

6,521.78 

94 

295.703 

6,958.26 

97 

305.128 

7,408.89 

91* 

286.671 

6,539.68 

296.096 

6,976.76 

97 

305.521 

7,427.97 

9H 

287.064 

6,557.61 

94 

296.488 

6,995.28 

97 

305.913 

7,447.08 

91} 

287.456 

6,575.56 

94 

296.881 

7,013.82 

97 

306.306 

7,466.21 

91} 

287.849 

6,593.54 

94 

297.274 

7,032.39 

97 

306.699 

7,485.37 

911 

288.242 

6,611.55 

94 

297.667 

7,050.98 

97 

307.091 

7,504.55 

91} 

288.634 

6,629.57 

94t 

• 

298.059 

7,069.59 

97 

307.484 

7,523.75 

92 

289.027 

6,647.63 

95 

298.452 

7,088.24 

98 

307.877 

7,542,98 

289.420 

6,665.70 

95 

298.845 

7,106.90 

98 

308.270 

7,562.24 

92* 

289.813 

6,683.80 

95; 

299.237 

7,125.59 

98 

308.662 

7,581.52 

92} 

290.205 

6,701.93 

95 

299.630 

7,144.31 

98 

309.055 

7.600.82 

92} 

290.598 

6,720.08 

95 

300.023 

7,163.04 

98 

309.148 

7,620.15 

92} 

290.991 

6,738.25 

95 

300.415 

7,181.81 

98 

309.840 

7,639.50 

92J 

291.383 

6,756.45 

95 

300.808 

7,200.60 

98 

310.233 

7,658.88 

92} 

291.776 

6,774.68 

95 

301.201 

7,219.41 

98 

- 

310.626 

7,678.28 

93i 

292.169 

6,792.92 

96 

301.594 

7,238.25 

99 

311.018 

7,697.71 

292.562 

6,811.20 

96 

301.986 

7,257.11 

99i 

311.411 

7,717.16 

93* 

292.954 

6,829.49 

96; 

302.379 

7,275.99 

99! 

311.804 

7,736.63 

93} 

293.347 

6,847.82 

96 

302.772 

7,294.91 

99} 

312.1% 

7,756.13 

93} 

293.740 

6,866.16 

96 

303.164 

7,313.84 

99} 

312.589 

7,775.66 

93} 

294.132 

6,884.53 

96 

303.557 

7,332.80 

99} 

312.982 

7,795.21 

93} 

294.525 

6,902.93 

96 

303.950 

7,351.79 

99} 

313.375 

7,814.78 

93} 

294.918 

6,921.35 

96} 

304.342 

7,370.79 

99} 

313.767 

7,834.38 

94 

295.310 

6,939.79 

97 

304.735 

7,389.83 

100 

314.160 

7,854.00 

DENOMINATE  NUMBERS 

A  denominate  number  is  one  expressed  in  units  of  a  certain  kind;  as,  for 
example,  5  days,  8  men,  etc. 

A  compound  denominate  number  is  one  expressed  in  two  or  more 
units;  as  3  hr.  20  min.,  8-ton  mi.,  4-acre-ft.,  etc.  The  terms  ft.  per  sec., 
mi.  per  hr.,  rev.  per  min.,  etc.,  are  all  compound  units. 

An  abstract  number  is  any  number  not  expressed  in  units  of  a  kind; 
as  3,  5,  8,  etc. 

Kinds  of  Units. — The  principal  kinds  of  units  may  be  classed  as  follows : 

1.  Units  of  weight;  as  tons,  pounds,  ounces,  grains,  etc. 

2.  Units  of  length  or  distance;  as  miles,  feet,  inches,  etc. 

3.  Units  of  volume ;  as  cubic  yards,  cubic  feet,  etc. 

4.  Units  of  capacity ;  as  gallons,  quarts,  pints,  etc. 

5.  Units  of  surface  or  area;  as  square  miles,  square  feet,  etc. 

6.  Units  of  time ;  as  years,  months,  days,  hours,  etc. 

7.  Units  of  circular  measure ;  as  degrees,  minutes,  etc. 

8.  Units  of  currency ;  as  dollars,  dimes,  cents,  etc. 

WEIGHTS  AND  MEASURES 

Systems  in  Use. — There  are  two  systems  of  weights  and  measures  in 
general  use,  known  as  the  "English,  United  States  or  British,"  and  the 
"  French  or  metric"  systems. 

The  basis  of  comf  arison  of  the  English  and  French  systems  is 
expressed  by- the  following  established  values: 

Weight. — The  pound  (7,000  grs.)  is  the  same  in  the  United  States  and 
Great  Britain.  The  pound  avoirdupois  is  equal  to  453.5924277  grams  in 
the  French  system. 

Length. — (United  States)  The  length  of  the  meter,  by  act  of  Congress, 
is  39.37  in.  (Great  Britain)  The  length  of  the  meter,  by  act  of  Parlia- 
ment, is  39.37079  in. 

The  slight  difference  in  the  length  of  the  meter,  as  established  by  law 
in  the  United  States  and  in  Great  Britain,  makes  the  English  inch  and 
yard  proportionally  shorter  than  the  same  units  in  the  United  States. 

Capacity. — The  gallon  and  liter  are  the  accepted  units  of  comparison 
in  the  English  and  French  systems,  respectively.  The  United  States  or 
"Winchester  gallon,"  however,  is  quite  different  from  the  "Imperial 
gallon"  of  Great  Britain,  which  was  made  the  volume  of  10  Ib.  of  distilled 
water,  at  maximum  density  (4  deg.  C.),  weighed  with  brass  weights  in 
air  at  62  deg.  F.,  barometer  30  in. 

Since  1  cu.  in.  pure  water,  under  the  same  conditions,  weighs  252.458 

397 


398  MINE  GASES  AND  VENTILATION 

grs.  and  1  Ib.  =  7,000  grs.,  the  volume  of  the  imperial  gallon  of  Great 
Britain  is 

10  X  7000 


The  volume  of  the  Winchester  gal)  on  of  the  United  States  is  231  cu.  in. 
The  French  liter  is  the  volume  of  1  kg.  of  distilled  water,  at  4  deg.  C., 
weighed  in  a  vacuum,  or  1,000  c.c.,  which  gives 

Winchester  gallon  (United  States),       231  cu.  in.  =  3.78543  liters. 

Imperial  gallon  (Great  Britain),  277.274  cu.  in.  =•  4.54346  liters. 

UNITED  STATES  AND  BRITISH  SYSTEMS 

Following  are  the  more  useful  of  the  tables  of  weights  and  measures  in 
the  English  system  : 

AVOIRDUPOIS  WEIGHT 

(  United  States) 

16  drams  =  1  ounce  ....................       437  .  5  pounds 

16  ounces  =  1  pound  ....................    7,000      grains 

25  pounds  =  1  quarter  ...................       400      ounces 

4  quarters  =  1  hundredweight  ...........  .       100      pounds 

20  hundredweight  =  1  short  ton  ................  ...    2,000      pounds 

(Greet  Britian) 

28  pounds  =  1  quarter  ...................       448      ounces 

4  quarters  =  1  hundredweight  .............       112      pounds 

20  hundredweight  =  1  long  ton  ..................    2,240      pounds 

The  short  ton  (2,000  Ib.)  is  more  generally  used  in  the  United  States, 
although  the  long  ton  (2240  Ib.)  is  used  at  times. 

TROY  WEIGHT 

24  grains  =  1  pennyweight 

20  pennyweights  =  1  ounce  ............................       480  grains 

12  ounces  =  1  pound  ............................    5,760  grains 

APOTHECARIES  WEIGHT 
20  grains  =  1  scruple  ...................... 

3  scruples  =  1  dram  ........................         60  grains 

8  drams  =  1  ounce  .......................       480  grains 

12  ounces  =  1  pound  .......................    5,760  grains 

The  grain  (troy)  is  the  same  as  the  grain  (apothecaries)  and  is  the  basis 
of  comparison  of  these  and  avoirdupois  weights.  Thus, 

1  Ib.  avoirdupois  =  7,000/5,760  =  1.21528  Ib.  troy. 
1  Ib.  troy  =  5,760/7,000  =  0.822857  Ib.  avoirdupois. 
1  oz.  avoirdupois  =  437.5/480  =  0.911458  oz.  troy. 
1  oz.  troy  =  480/437.5  =  1.097143  oz.  avoirdupois. 


DENOMINATE  NUMBERS  399 

LONG  MEASURE 

12  inches  =  1  foot 

3  feet  =  1  yard 36    inches 

5>^  yards  =  1  rod,  perch,  or  pole 16^  feet 

40  rods  =  1  furlong 660      feet 

8  furlongs  =  1  mile 5,280      feet 

3  miles  =  1  league 

The  old  surveyor's  chain  of  100  links  (1  link  =  7.92  in.)  was  66  ft. 
long,  making  80  chains  =  1  rni.  Chains  now  in  common  use  are  50,100 
and  300  ft.  long,  made  up  of  1-ft.  links. 

A  fathom  is  6  ft.  or  2  yd.,  used  in  estimating  depth. 

SQUARE  MEASURE 

144  sq.  inches  =  1  square  foot 

9. square  feet  =  1  square  yard 1296  square  inches 

30K  square  yards  =  1  square  rod 272  Y±  square  feet 

40  square  rods  =  1  rood 10,890  square  feet 

4  roods  =  1  acre 43,560  square  feet 

640  acres  =  1  square  mile 102,400  square  rods 

An  acre  contains  43,560  sq.  ft.  and  measures  208.7  ft.  on  each  side; 
\/437560  =  208.7  ft. 

CUBIC  MEASURE 
1728  cubic  inches  =  1  cubic  foot 

27  cubic  feet        =  1  cubic  yard 46,656  cubic  inches 

16  cubic  feet       =  1  cord  foot 27,648  cubic  inches 

8  cord  feet         =  1  cord 128  cubic  feet 

A  cord  of  wood  is  a  pile  8  ft.  long,  4  ft.  wide  and  4  ft.  high,  and  contains 
8  X  4  X  4  =  128  cu.  ft. 

A  cord  foot  is  one  foot  of  the  length  of  the  pile  that  makes  a  cord, 
and  contains  1  X  4  X  4  =  16  cu.  ft. 

A  ton  of  round  timber  (green)  is  taken  as  50  cu.  ft. 

A  ton  of  squared  timber  (green)  is  40  cu.  ft.,  it  being  assumed  that 
hewed  or  squared  timber  has  lost  one-fifth  of  its  original  volume  in 
squaring. 

A  long  ton  (2,240  Ib.)  of  anthracite  or  a  short  ton  (2,000  Ib.)  of  bitumi- 
nous coal  broken  (mine-run)  occupies  about  40  cu.  ft. 

There  are  two  measures  of  capacity,  known  as  "Liquid"  and  "Dry" 
measures,  having  like  denominations  but  of  different  values.  The  old 
English  wine  gallon  (231  cu.  in.)  was  replaced  in  England,  in  1824,  by  the 
imperial  gallon  (277.274  cu.  in.),  but  is  still  the  standard  "Winchester" 
gallon  in  the  United  States.  The  "Dry  "  gallon,  now  practically  obsolete, 
contained  268.8  cu.  in. 


400  MINE  GASES  AND  VENTILATION 

LIQUID  MEASURE  (U.  S.) 


4    gills              =  1  pint  

28  875  cubic  inches 

2    pints            =  1  quart 

.  .    .  .          57  75    cubic  inches 

4    quarts          =  1  gallon 

231           cubic  inches 

1^  gallons         =  1  barrel  

4  21    cubic  feet 

2    barrels         =  1  hogshead  
2    hogsheads  =  1  pipe 

63          gallons 
126           gallons 

2    nioes             =  1  tun  .  . 

8          barrels 

DRY  MEASURE  (U.  S.) 

2  pints       =  1  quart 67. 2  cubic  inches 

8  quarts    =  1  peck 537. 6  cubic  inches 

4  pecks      =  1  bushel 2150. 4  cubic  inches 

36  bushels  =  1  chaldron 44 . 8  cubic  feet 

Or,    4  quarts    =  1  gallon 268 . 8  cubic  inches 

8  gallons   =  1  bushel 2150. 4  cubic  inches 

The  standard  bushel,  in  the  United  States,  is  the  old  Winchester 
bushel,  which  is  a  circular  measure  18^  in.  in  diameter  and  8  in.  deep, 
containing  8  (0.7854  X  18.52)  =  2150.4  cu.  in.  This  was  replaced  in 
England,  in  1826,  by  the  imperial  bushel  (2218.192  cu.  in.),  which  was 
then  made  the  legal  bushel. 

LIQUID  AND  DRY  MEASURE   (GREAT  BRITAIN) 

4  gills        =  1  pint 34 . 659  cubic  inches 

2  pints      =  1  quart 69.318  cubic  inches 

4  quarts    =  1  gallon 277 . 274  cubic  inches 

2  gallons  =  1  peck 554 . 548  cubic  inches 

4  pecks     =  1  bushel 2218. 192  cubic  inches 

There  is  no  separate  standard  for  liquid  and  dry  measures  in  Great 
Britain,  both  being  referred  to  the  same  unit  or  standard,  which  is  the 
imperial  gallon  (277.274  cu.  in.). 

MEASURE  OF  TIME 

60  seconds  =  1  minute 

60  minutes  =  1  hour 

24  hours  =  1  day 

7  days  =  1  week 

365  days  =  1  common  year 

366  days  =  1  leap  year 

12  calendar  months  =  1  calendar  year 
100  years  =  1  century 

Commonly  speaking,  a  day  is  marked  by  one  complete  revolution 
of  the  earth  on  its  axis,  and  a  year  by  one  revolution  of  the  earth  in  its 
orbit  about  the  sun.  Unfortunately,  however,  the  earth  does  not  make 
an  even  number  of  turns  on  its  axis,  while  making  one  complete  revo- 


DENOMINATE  NUMBERS  401 

lution  in  its  orbit.     There  are  approximately  365^  revolutions  on  the 
axis  to  a  single  revolution  in  the  orbit. 

In  order  to  compensate  for  this  eccentricity  and  make  the  calendar 
year  conform  as  closely  as  possible  to  the  solar  year,  so  as  to  preserve 
uniformity  in  the  return  of  the  seasons,  it  was  necessary  to  add  one  day 
to  the  calendar  every  fourth  year,  except  the  closing  year  of  the  century. 
Thus,  the  common  year  of  365  days  was  supplemented  by  a  leap  year 
containing  366  days. 

The  "Gregorian"  calendar,  established  by  Pope  Gregory  XIII  (1582) 
and  generally  adopted  in  Great  Britain  and  elsewhere  (1752),  replaced  the 
"Julian"  calendar  and,  in  dropping  10  days  by  making  Oct.  5,  Oct.  15, 
1582,  restored  the  equinoxes  to  their  proper  date.  To  obtain  closer 
correspondence  of  the  calendar  and  solar  years,  the  closing  year  of  each 
century,  1600,  1700,  etc.,  was  made  a  common  year,  although  these 
would  be  leap  years  in  the  regular  course. 

The  Day. — A  day  is  the  interval  of  time  marked  by  two  successive 
transits  of  a  heavenly  body  across  a  given  meridian,  caused  by  the  revolu- 
tion of  the  earth  on  its  axis. 

The  solar  day  (24  hr.,  0  min.)  is  the  time  interval  marked  by  two  suc- 
cessive transits  of  the  sun  across  the  meridian. 

The  sidereal  day  (23  hr.,  56  min.)  is  the  time  interval  marked  by  two 
successive  transits  of  a  fixed  star  across  a  given  meridian. 

The  Month. — The  calendar  year  has  been  arbitrarily  divided  into  12 
months,  in  correspondence  to  the  "number  of  moons"  or  the  revolutions 
of  the  moon  about  the  earth  in  a  solar  year.  But,  since  365  days  are  not 
equally  divisible  by  12,  it  was  necessary  to  make  an  unequal  division,  as 
follows: 

January    31  days  May      31  days  September  30  days 

February  28  days  June      30  days  October       31  days 

March       31  days  July       31  days  November  30  days 

April         30  days  August  31  days  December  31  days 

The  extra  day  required  in  a  leap  year  is  added  to  the  month  of  Feb- 
ruary, making  29  days  in  that  month  every  leap  year,  instead  of  28  as  in 
the  common  year. 

The  Year. — A  year  is  the  period  of  time  in  which  the  earth  completes 
one  revolution  in  its  orbit. 

The  solar  year  (365  d.,  5  hr.,  48  min.,  45.51  sec.)  marks  a  complete 
revolution  about  the  sun. 

The  sidereal  year  (365  d.,  6  hr.,  9  min.,  8.97  sec.)  marks  a  complete 
revolution  with  respect  to  a  fixed  star. 

CIRCULAR  MEASUBH 
60  seconds  =  1  minute 

60  minutes  =  1  degree 3,600  seconds 

15  degrees   =  1  hour  angle 900  minutes 

30  degrees  =  1  sign 1,800  minutes 

12  signs       =  1  great  circle  or  circumference 360  degrees 

26 


402  MINE  GASES  AND  VENTILATION 

The  "sign"  is  one  of  the  twelve  divisions  of  the  zodiac,  which  corre- 
spond to  the  twelve  calendar  months  of  the  year.  The  sign  has  no 
practical  value  technically. 

It  is  often  convenient  to  express  the  length  of  an  arc,  or  the  angle  it 
subtends,  in  terms  of  the  radius  of  the  circle.  In  that  case,  the  unit  of 
length  is  called  a  "radian."  A  radian  is  a  length  of  arc  equal  to  the 
describing  radius.  Its  value  expressed  in  degrees  is  180°  -f-  TT  = 
180/3.14159  =  57.2958  deg.,  or  57°  17'  44.88".  Since  the  length  of  the 
circumference  of  a  circle  is  2irr,  there  arc  2-n-  radians  in  a  circumference  or 
360  deg. 

Circular  measure  is  used  in  the  measurement  of  angles  and  in  the  esti- 
mation of  latitude,  longitude  and  solar  or  sun  time,  which  varies  from 
standard  time  according  to  the  location  of  the  observer. 

Measurement  of  Time. — The  passing  of  time  is  measured  1  y  the 
revolution  of  the  earth  on  its  axis,  as  determined  by  the  observation  of 
the  sun  or  one  of  the  fixed  stars  when  crossing  the  meridian  of  a  place. 
A  single  revolution  of  the  earth  marks  a  period  of  24  hr.  or  one  day. 

Sun  Time. — Owing  to  the  inclination  of  the  earth's  axis  to  the  plane 
of  its  orbit  and  the  eccentricity  of  the  orbit,  the  sun's  apparent  motion 
in  the  celestial  sphere  is  not  wholly  uniform,  on  which  account  solar  time 
is  referred  to  a  "  mean  sun"  having  an  assumed  uniform  motion. 

Equation  of  Time. — The  difference  between  the  mean  sun  and  the  true 
or  observed  sun,  expressed  in  hours,  minutes  and  seconds,  is  called 
the  "  equation  of  time."  This  is  found  for  any  date  in  the  "Ephemeris" 
or  Nautical  Almanac. 

Sidereal  Time. — The  apparent  movement  of  the  fixed  stars,  unlike 
that  of  the  sun,  is  uniform,  which  makes  the  sidereal  day  correspond 
precisely  with  one  complete  revolution  of  the  earth  on  its  axis.  About 
Mar.  21,  or  at  the  vernal  equinox,  sidereal  time  agrees  with  mean  sun  or 
solar  time. 

Local  Time. — When  the  24-hr,  cycle  is  referred  to  the  local  meridian  as 
zero  (noon  or  midnight)  the  indicated  hour  is  the  local  time,  or  the  time 
for  that  place  only.  Since  there  are  360  deg.  in  a  circle,  which  marks 
1  day  or  24  hr.  of  the  celestial  equator,  1  hr.  corresponds  to  360  -r-  24  = 
15  deg.  Hence,  a  difference  of  15  deg.  marks  a  difference  of  1  hr.  in  local 
time. 

Longitude,  Latitude. — Longitude  is  the  distance  either  east  or  west  of 
the  meridian  of  Greenwich,  which  is  marked  by  the  Royal  Observatory, 
and  measured  in  degrees,  minutes  and  seconds,  on  the  equator.  There 
are  thus  180  deg.  of  east  longitude  and  180  deg.  of  west  longitude. 

Latitude  is  likewise  distance  north  or  south  of  the  equator,  measured 
in  degrees,  minutes  and  seconds,  on  any  meridian  or  great  circle  passing 
through  the  poles.  There  are  thus  90  deg.  of  north  latitude  and  90  deg. 
of  south  latitude. 

Standard  Time. — To  obviate  the  confusion  caused  by  the  difference 
in  local  time,  a  system  of  "standard  time"  has  been  adopted.  Starting 


DENOMINATE  NUMBERS  403 

from  the  meridian  of  Greenwich,  standard  time  is  1  hr.  later  for  each 
15  deg.  of  east  longitude,  and  1  hr.  earlier  for  each  15  deg.  of  west  longi- 
tude. Calling  the  equatorial  circumference  of  the  earth  25,000  mi.,  a 
degree  of  longitude  represents  a  distance  on  the  equator  of  25,000  -=- 
360  =  69.4  mi.  One  hour  (15  deg.)  corresponds  to  a  distance  of 
practically  1,000  mi.  at  the  equator. 

In  the  United  States  and  Canada,  there  are  four  divisions  of  standard 
time,  known  as  Eastern,  Central,  Mountain  and  Pacific  time,  which  are 
exactly  1  hr.  apart.  These  are  all  referred  to  the  observatory  at  Green- 
wich, which  marks  the  zero  of  longitude. 

Eastern  time  is  the  solar  time  of  the  meridian  75  deg.  west  longitude, 
and  is  the  standard  time  for  all  places  within  7}$  deg.  on  either  side  of  that 
meridian.  Eastern  time  is  therefore  75  -5-  15  =  5  hr.  earlier  than  Green- 
wich 'time. 

Central  time  is  solar  time  for  the  meridian  90  deg.  west  longitude,  and 
is  likewise  standard  for  all  places  within  7%  deg.  east  or  west  of  that 
meridian.  Central  time  is  1  hr.  earlier  than  Eastern  time. 

Mountain  time  is  solar  time  for  the  meridian  105  deg.  west  longitude 
and  standard  for  all  places  within  7  3^  deg.  east  or  west  of  that  meridian. 
Mountain  time  is  1  hr.  earlier  than  Central  time. 

Pacific  time  is  solar  time  for  the  meridian  120  deg.  west  longitude  and 
standard  for  all  places  within  7%  deg.  east  or  west  of  that  meridian. 
Pacific  time  is  1  hr.  earlier  than  Mountain  time. 

When  it  is  noon  at  the  observatory  at  Greenwich  it  is  7  a.m.  at  New 
York,  6  a.m.  at  Chicago,  5.  a.m.  at  Denver  and  4  a.m.  at  San  Francisco. 
At  the  same  time  it  is  1  p.m.  at  Berlin  and  Rome,  2  p.m.  at  Petrograd 
and  8  p.m.  in  the  Philippines. 

Civil  Time. — The  day,  for  all  common  purposes  of  reckoning,  begins 
and  ends  at  midnight.  The  24  hr.  are  divided  into  two  periods  of  12  hr. 
each.  The  hours  from  midnight  to  noon  are  designated  by  the  letters 
a.m.  (ante  meridian),  and  those  from  noon  to  midnight  by  the  letters 
p.m.  (post  meridian). 

Astronomical  Time. — The  astronomical  day  is  reckoned  from  noon  to 
noon,  the  hours  being  counted  from  1  to  24.  The  astronomical  day  begins 
12  hr.  later  than  the  civil  day,  as  the  following  comparisons  will  show: 

Civil  time,  Nov.  6,  3  a.m.;  Nov.  6,  3  p.m.;  Nov.  7,  3  a.m. 

Astronomical  time,  Nov.  5,  15  hr.;  Nov.  6,  3  hr.;  Nov.  6,  15  hr 

METRIC  SYSTEM  OF  WEIGHTS  AND  MEASURES 

The  units  of  the  metric  system  are  the  gram,  meter  and  liter.  The 
system,  unlike  that  of  the  United  States  and  Great  Britain  is  wholly 
a  decimal  system  and,  for  that  reason,  is  more  convenient  for  use. 

Denominations. — The  higher  denominations  of  weight,  length  and 
capacity  are  obtained  by  multiplying  each  respective  urflt  by  10,  100, 


404  MINE  GASES  AND  VENTILATION 

1000,  etc.,  while  lower  denominations  than  the  unit  are  likewise  obtained 
by  dividing  the  same  by  10,  100  or  1000. 

The  denominations  of  the  metric  system  are  expressed  by  the  Latin 
and  Greek  prefixes,  the  former  being  used  to  indicate  divisions  of  the 
unit,  while  the  latter  are  employed  to  express  multiples  of  the  same 
unit.  These  prefixes  and  their  respective  values  are  as  follows: 

Milli,     1/1000 1  milligram  (mg.)  =  0. 001  gram 

Centi,    1/100 1  centigram  (eg.)  =0.01  gram 

Deci,      1/10 1  decigram  (dg.)  =0.1  gram 

Unit  of  Weight 1  gram 

Deca,     10 1  decagram  =  10  grams 

Hecto,  100 1  hectogram  =  100  grams 

Kilo,      1000 1  kilogram  (kg.)  =1000  grams 

Myria,  10,000 1  myriagram  =  10,000  grams 

The  same  prefixes  are  used  to  express  similar  divisions  and  multiples 
of  the  units  of  length  and  capacity.  Area  and  volume  are  expressed  by 
the  words  square  and  cubic  preceding  the  same  denominations  of  length. 
Following  are  the  tables  of  the  metric  system  and  equivalents : 

METRIC  WEIGHT 

10  milligrams     =  1  centigram 0. 15432356    gr.  (troy) 

10  centigrams     =  1  decigram 1 . 54323564    gr. 

10  decigrams      =  1  gram 15 . 43235639    gr. 

0.03527396    oz.  (avdp.) 

10  grams  =  1  decagram 0. 35273957    oz. 

10  decagrams     =  1  hectogram 3.52739575    oz. 

10  hectograms    =  1  kilogram 35.27395746    oz. 

2.20462234    Ib. 
10  kilograms       =  1  myriagram 22 . 04622341    Ib. 

0.22046223  cwt. 

10  myriagrams  =  1  quintal 2 . 20462234  cwt. 

10  quintals          =  1  tonne 1 . 10231117  tons 

The  French  tonne  (2204.6  Ib.)  differs  but  slightly  from  the  British  long 
ton  (2240  Ib.) 

METRIC  LENGTH 

10  millimeters    =  1  centimeter 0.3937  inches 

10  centimeters   =  1  decimeter 3.937    inches 

10  decimeters     =  1  meter 39 . 37      inches 

3.2808      feet 

10  meters  =  1  decameter 32 . 8083       feet 

10  decameters    =  1  hectometer 328 . 0833      feet 

0.0621    miles 
10  hectometers  =  1  kilometer 0. 6214    miles 

The  Austrian,  Prussian,  Danish  and  Norwegian  mile  is  equal  to  about 
4.7  American  miles;  the  Swedish,  to  about  6%  American  miles;  while  the 
Russian  "verst"  is  3500  ft. 


DENOMINATE  NUMBERS  405 

METRIC  AREA 

100  sq.  millimeters   =  1  sq.  centimeter 0. 155  sq.  in. 

100  sq.  centimeters  =  1  sq.  decimeter 15.500  sq.  in. 

100  sq.  decimeters    =  1  sq.  meter  (centare) 1549 . 997  sq.  in. 

10.764   sq.  ft. 

100  centares  =  1  sq.  decameter  (are) 1076. 387    sq.  ft. 

0.025     acres 
100  ares  =  1  sq.  hectometer  (hectare).  .  .          2.471     acres 

100  hectares  =  1  sq.  kilometer 247. 104     acres 

0.386  sq.  mi. 
100  sq.  kilometers     =  1  sq.  myriameter 38.610  sq.  mi. 

The  unit  of  area  is  the  square  meter  or  centare. 

METRIC  VOLUME 

1000  cu.  millimeters   =  1  cu.  centimeter 0.061   cu.  in. 

1000  cu.  centimeters  =  1  cu.  decimeter 61 . 023   cu.  in. 

1000  cu.  decimeters    =  1  cu.  meter 35 . 314   cu.  ft. 

1 . 308  cu.  yd. 

The  weight  of  1  cu.  centimeter  of  distilled  water  at  maximum  density 
(4°C.),  weighed  in  a  vacuum,  is  1  gram;  or  1  cu.  decimeter  of  same  under 
like  conditions  is  1  kilogram. 

METRIC  CAPACITY 

10  milliliters      =  1  centiliter 0. 610  cu.  in. 

10  centiliters      =  1  deciliter 6 . 102  cu.  in. 

10  deciliters       =  1  liter. 61 .023  cu.  in. 

0.035  cu.  ft. 

10  liters              =  1  decaliter  (centistere) 0 . 353  cu.  ft. 

10  centisteres     =  1  hectoliter  (decistere) 3.531  cu.  ft. 

10  decisteres      =  1  kiloliter  (stere) 35. 314  cu.  ft. 

10  steres             =  1  myrialiter  (decastere) .  .  353. 145  cu.  ft. 

The  liter  is  the  unit  of  capacity  in  the  metric  system.  Its  volume  is 
1000  cu.  centimeters  or  1  cu.  decimeter.  It  contains  61.02338189  cu.  in., 
or  0.26417  gal.  (Winchester).  Or  a  single  Winchester  gallon  contains 
3.785434  liters. 

The  Fluid  Ounce. — What  is  known  as  the  "fluid  ounce"  is  a  quantity 
of  any  liquid  equal  to  that  of  pure  water  at  maximum  density  (4°C.) 
and  weighing  exactly  1  oz.  avoirdupois.  The  volume  of  the  fluid  ounce 
is  calculated  as  follows: 

1  cubic  centimeter  of  water  (4°C.)  =  1  gram. 

1  ounce  avoirdupois  =  437.5  grains. 

1  gram  =  15.43236  grains. 

Hence,  since  the  volume  of  1  gram  (water)  is  1  c.c.  and  the  fluid  ounce 


406  MINE  GASES  AND  VENTILATION 

has  a  volume  based  similarly  on  the  avoirdupois  ounce,  the  value  of  the 
fluid  ounce  is 

437  ^ 
Fluid  ounce  (fl.  oz.),  =  28.3495  c.c. 


The  minim  (a  drop),  the  smallest  liquid  measure,  is  Ko  of  a  fluid  dram 
or  the  equivalent  in  volume  of  1  grain,  which  is  1  -5-  15  .  43236  =  0.0648  c.c.  ; 
or  28.3495  -f-  437.5  =  0.0648  c.c. 

Metric  Abbreviations.  —  The  following  are  the  common  abbreviations 
used  in  the  metric  system: 

Milligram,  mg.;  millimeter,  mm.jmilliliter,  ml. 
Centigram,  eg.  ;  centimeter,  cm.;  centiliter,  cl. 
Decigram,  dg.;  decimeter,  dm.;  deciliter,  dl. 
Gram,  g.  ;  meter,  m.;  liter,  1. 

Kilogram,    kg.  ;  kilometer,    km.  ;  kiloliter,     kl. 
Square  millimeter,  mm2;  cubic  millimeter,  mm3. 
Square  centimeter,  cm2;  cubic  centimeter,   cm3. 
Square  decimeter,    dm2;  cubic  decimeter,    dm3. 
Square  meter,  m2;  cubic  meter,  m3. 

Square  kilometer,     km2. 

Compound  Units.  —  It  is  often  convenient  to  express  values  involving 
two  or  more  denominations  in  terms  of  a  single  compound  unit.  The 
following  are  examples  of  such  compound  units: 

Work  is  expressed  as  a  force  (pounds)  exerted  through  a  distance 
(feet)  and  its  unit,  therefore,  combines  both  of  these  denominations, 
giving  foot-pounds  (ft.-lb.),  or  inch-pounds  (in.-lb.),  as  the  case  may  be. 

Power  is  expressed  as  work  performed  per  unit  of  time,  as  foot-pounds 
per  minute  (ft.-lb.  p.m.),  or  per  second  (ft.-lb.  p.s.). 

In  like  manner,  the  speed  of  rotatien  is  given  in  revolutions  per  minute 
(r.p.m.);  or  the  speed  of  a  train  as  miles  per  hour  (mi.  p.  hr.);  or  the 
velocity  of  an  air  current  as  cubic  feet  per  minute  (cu.  ft.  p.  m.). 

It  is  common  to  estimate  the  value  of  coal  lands  in  tons  per  acre,  or 
acre-tons;  or  to  express  the  amount  of  underlying  coal  in  acre-feet, 
which  combines  in  a  single  unit  both  the  acreage  of  the  seam  and  the 
average  thickness  of  the  coal  in  feet. 

CONVERSION  TABLES 

Numerous  forms  of  tables  are  in  use  for  converting  denominations  of 
the  United  States  system  into  the  corresponding  denominations  of  the 
metric  system  and  vice  versa,  but  the  following  are  believed  to  best 
serve  the  purpose.  For  the  sake  of  more  ready  reference,  the  denomina- 
tions of  weight,  length,  area,  volume  and  capacity  are  here  given  in 
separate  tables,  and  the  values  given  in  the  tables  are  simple  multipliers: 


DENOMINATE  NUMBERS 


407 


AVOIRDUPOIS  (METRIC  TO  U.  S:) 


1 
1 
1 

1 
1 
I 
1 
I 
1 
1 

milligram 
centigram 
decigram 
gram 
decagram 
hectogram 
kilogram 
myriagram 
quintal 
tonne 

Drams         ( 
=       0.00056 
=      0.0056 
=   ,   0.0564 
=      0.564       0 
=      5.644       0 
=56.438      3. 
=  564.38      35. 

)unce 

035 
353 
527 
274 

Pounds 


0.0022 
0.022 
0.220 
2.205 
22 . 046 
220.46 


Tons 


0.0011 
0.0110 

0.1102 


2204.62        1.1023 
When  closer  determinations  are  desired  the  values  given  in  the  metric 
tables  should  be  employed. 

AVOIRDUPOIS  (U.  S.  TO  METRIC) 

Grams 

1.77 
28.35 
453 . 59 


Kilograms 


1  dram  = 

1  ounce  = 

1  pound  = 

1  ton  = 


Milligrams 

1771.8 

0.02835 
0.4536 
907.184 
TROY  ( METRIC  TO  U.  S.) 

Penny 


Tonne 


0.90718 


Grains 

weights 

Ounces 

Pounds 

1  milligram 

= 

0 

0154 

1  centigram 

= 

0 

154 

0 

006 

1  decigram 

= 

1 

54 

0. 

064 

0. 

0032 

1  gram 

= 

15. 

43 

0. 

643 

0. 

032 

1  decagram 

= 

6. 

430 

0 

322 

0 

,0268 

1  hectogram 

BS 

64. 

302 

3 

215 

0 

.2679 

1  kilogram 

= 

32 

151 

2 

.679 

1  myriagram 

« 

26 

.79 

grain 
pennyweight 


1  ounce 
1  pound 


1  milligram  = 
1  centigram  = 
1  decigram  = 
1  gram  = 

1  decagram  = 
1  hectogram  = 
1  kilogram  = 


TROY  (U.  S.  TO  METRIC) 

Milligrams-  Grams 

=  64.8  0.065 

1.555 

31.103 


APOTHECARIES  (METRIC  TO  U. 

Grains  Scruples  Drams 

0.0154 

0.154    0.0077 

1.54  0.077  0.026 

15.43  0.772  0.257 

7.72  2.57 


S.) 

Ounces 


0.032 
0.322 
3.215 
32.15 


Kilograms 

0.031 
0.373 

Pounds 


0.268 
2.679 


408 


MINE  GASES  AND  VENTILATION 


1  grain  = 

1  scruple  = 

1  dram  = 

1  ounce  = 

1  pound  = 


1  millimeter 
1  centimeter 
1  decimeter 
1  meter 
1  decameter 
1  hectometer 
1  kilometer 


APOTHECARIES  (U.  S.  TO  METRHC) 

Milligrams  Grams 

64.8         0.065 

1.296 

3.888 

31.103 


LINEAR  (METRIC  TO  U.  S.) 


Kilograms 


0.031 
0.373 


1  myriameter 


Inches 

Feet 

Yards 

Rods 

Miles 

0.039 

0.39 

0.033 

3.94 

0.33 

39.37 

3.28 

1.094 

0.199 

32.81 

10.936 

1.988 

0.0062 

109.36 

19.884 

0.0621 

0.6214 

6.2137 

The  old  surveyor's  chain  (66  ft.)  contains  20.1168  meters,  and  one 
kilometer    (3280.83    ft.)    is    49.71    of    such    chains. 


LINEAR  (U.  S.  TO  METRIC) 


1  inch 
1  foot 
1  yard 
1  rod 
1  furlong 
1  mile 


Millimeters 

25.400 
304.800 


Centimeters 

2.540 
30.480 
91.440 


Meters 

0.0254 
0.3048 
0.914 
5.029 
201 . 168 
1609.347 


Kilometers 


0.005 
0.201 
1.609 


SQUARE  (METRIC     TO  U.   S.) 


Sq 

.  in.              Sq.  ft. 

1  sq.  millimeter 

=     0. 

0015 

1  sq.  centimeter 

=     0. 

155 

1  sq.  decimeter 

=    15. 

500         0. 

108 

1  sq.  meter 

= 

10. 

764 

(centare) 

1  sq.  decameter 

= 

1076 

.387 

(are) 

1  sq.  hectometer 

= 

, 

(hectare) 

1  sq.  kilometer 

= 

1  sq.  myriameter 

= 

Sq.  rods         Acres         Sq.  mi. 


0.040 

3.954   0.025 
395.367   2.471 

247.104  0.386 
38.61 


DENOMINATE  NUMBERS  409 

SQUARE  (U.  S.  TO  METRIC) 

Sq.  mm.         Sq.  cm.          Centares         Ares  Hectares 

sq.  inch  =       645.16  6.45 

sq.  foot  =  929 .03         0 . 093 

sq.  yard  =  0 . 836 

sq.  rod  =  25.293         0.253 

acre  40.469  0.405 

sq.  mile  =  259. 

CUBIC  (METRIC  TO  U.  S.) 

Cu.  inches     Cu.  feet  Cu.  yards 

1  cu.  millimeter  =  0 . 00006 

1  cu.  centimeter  =  0.06102 

1  cu.  decimeter  =  61.0235       0.0353         0.0013 

1  cu.  meter  35.3145         1.308 

CUBIC  (U.  S.  TO  METRIC) 

Cu.  mm.  Cu.  cm.  Cu.  dm.  Cu.  m. 

1  cu.  inch    =   16,387  16.387  0.016 

1  cu.  foot     =  28,316.84  28.317         0.028 

1  cu.  yard    =  764.555         0.765 

CAPACITY-  (METRIC  TO  U.  S.,  LIQUID) 

Gills         Pints         Quarts       Gallons     Barrels         Hhd. 

milliliter  =  0.008 

centiliter  =   0.085     0.021 

deciliter  =0.845     0.211       0.106 

liter  =  8.453     2.113       1.057       0.264 

decaliter  =  10.567       2.642     0.084 

hectoliter  =  26.417     0.839     0.419 

1  kiloliter  =  264.170     8.386     4.193 

1  myrialiter  =  83.864  41.932 

One  myrialiter  contains  10.48295  tuns. 

CAPACITY  (METRIC  TO  U.  S.,  DRY) 


1 

Pints 

centiliter    =  0.018 

Quarts 

Gallons 

Pecks 

Bushels 

1 

deciliter      =  0.182 

0. 

091 

1 

liter            =   1.816 

0 

.908 

0. 

227 

0 

,114 

0 

.028 

1 

centistere  = 

9, 

081 

2. 

270 

1 

.135 

0 

,284 

1 

decistere    = 

.' 

22. 

702 

11 

351 

2.838 

1 

stere           = 

28 

.378 

1 

decastere    = 

283. 

777 

The  decastere  is  equal  to  7.88269  chaldrons. 


410  MINE  GASES  AND  VENTILATION 

CAPACITY  (U.  S.  TO  METRIC) 


(Liquid)              Ml. 

Cl.                  Dl. 

L. 

Kl. 

gill             =    118.29 

11.829         1.183 

0.118 

pint 

47.318         4.732 

0.473 

quart         = 

9.464 

0.946 

gallon        = 

37.854 

3.785 

barrel         = 

119.241 

0.119 

hogshead  = 

238  .  482 

0.238 

pipe 

476.965 

0.477 

tun 

953.929 

0.954 

(Dry) 

pint            =   550.61 

55.061         5.506 

0.551 

quart          = 

110.122       11.012 

1.101 

gallon        = 

44.049 

4.405 

peck 

88.097 

8.810 

L  bushel        = 

35.239 

0.035 

1  chaldron    = 

1.269 

CAPACITY  (METRIC  TO  BRITISH) 

(Wet  and  dry)  Gills          Pints        Quarts          Gallons          Pecks  Bushels 


1 

1 

milliliter      =   0.007 
centiliter     =   0.070 

0.018 

1 

deciliter       =   0.704 

0.176     0.088 

0 

.022 

1 

liter              =   7.043 

1.761     0.880 

0 

.220 

0 

.110 

0 

.028 

1 

decaliter      = 

8.803 

2 

.201 

1 

.100 

0 

275 

1 

hectoliter     = 

22 

.008 

11 

.004 

2 

,751 

1 

kiloliter       = 

220 

083 

110, 

042 

27 

510 

1 

rnyrialiter    = 

275. 

104 

CAPACITY  (BRITISH  TO  METRIC) 

(Wet  and  dry)       Ml.  Cl.  Dl.  L.  Kl. 

1  gill  =  142.0         14.199           1.420           0.142 

1  pint  =  56.797           5.680           0.568 

1  quart  =  11.359           1.136 

1  gallon  =  45.437           4.544 

1  peck  =  90.875           9.087 

1  bushel  =  36.350         0.036 

The  conversion  factors  in  these  tables  have  been  derived  independently 
from  the  following  standards: 

1  meter  (U.  S.)  =  39.37  in.     (1  in.  =  25.4  mm.); 

1  sq.  meter  =  39.S72  -T-  144  =  10.76386736  sq.  ft.; 

1  cu.  meter  =  39.373  -=-  1728  =  35.31445447  cu.  ft.; 

1  liter  =  61.02338189  cu.  in.; 

1  U.  S.  (Winchester)  bushel  =  2150.4  cu.  in.; 

1  British  (Imperial)  bushel  =  2218.192  PU.  in. 


DENOMINATE  NUMBERS  411 

CONVERSION  OF  COMPOUND  UNITS 

In  the  conversion  of  compound  units  from  the  United  States  to  the 
metric  system,  and  vice  versa,  it  is  more  convenient  and  saves  much 
time  and  frequently  avoids  error  arising  from  confusion  of  terms  to  em- 
ploy a  single  factor.  The  following  are  the  more  common  conversion 
factors : 

WEIGHT  PER  UNIT  LENGTH 

1  Ib.  per  ft (0.4536  X  3.28)       =  1.488  kg.  per  m. 

1  Ib.  per  yd (0.4536  X  1.0936).  =  0.496    kg.  per  m. 

1  ton  per  mi (0.9072  X  0.6214)  =  0.5637  tonnes  per  km. 

1  long  ton  per  mi (1.016     X  0.6214)  =  0.6313  tonnes  per  km. 

WEIGHT  PER  UNIT  AREA 

1  Ib.  per  sq.  ft (0.4536  X  10.764)  =  4.882    kg.  per  m2 

1  ton  per  sq.  ft (0.9072  X  10.764)  =  9.765    tonnes  per  m2 

1  ton  per  sq.  yd (0.9072  X     1.196)   =  1.085    tonnes  per  m2 

1  ton  per  acre (0.9072  X    2.471)  =  2.2417  tonnes  per  hectare 

1  long  ton  per  acre (1.016    X    2.471)  =  2.5105  tonnes  per  hectare 

WEIGHT  PER  UNIT  VOLUME 
1  oz.  per  cu.  in    ...    (28.35     X  0.06102)  =  1.73  g.  per  cm3 

1  oz.  per  cu  .ft (0.0283  X  35.3145)  =  1.00  kg.  per  m3 

1  Ib.  per  cu.  ft (0.4536  X  35.3145)  =  16.0184  kg.  per  m3 

1  Ib.  per  cu.  yd. ...    (0.4536  X  1.308)       =  0.5933  kg.  per  m3 

1  ton  per  cu.  yd    .  .    (0.9072  X  1.308)       =  1.1866  tonnes  per  m3 

1  ton  per  acre-ft. .  .    (0.9072  X  8.106)       =  7.3538  tonnes  per  hectare-m. 

1  long  ton  per  acre-ft  (1.016     X  8. 106)       =  8. 2357  tonnes  per .  hectare-m . 

It  is  worthy  of  note  that  ounces  per  cubic  foot  are  equivalent  to  kilo- 
grams per  cubic  meter,  or  grams  per  liter,  since  1  m3  =  1000  liters. 

WEIGHT  PER  UNIT  CAPACITY — LIQUID 

1  gr.  per  gal.— U.  S (64.8    X  0.264)  =     17.107  mg.  per  1. 

1  oz.  per  gal (  28.35  X  0.264)  =      7.484  g.  per  1. 

1  Ib.  per  gal (453.59  X  0.264)  =  119.748  g.  per  1. 

1  gr.  per  gal.— Gt.   Br (64.8    X  0.22).    =     14.256  mg.  per  1. 

1  oz.  per  gal (28.35  X  0.22)     =       6.237  g.  per  1. 

1  Ib.  per  gal (453.59  X  0.22)     =    99.790  g.  per  1- 

WEIGHT  PER  UNIT  CAPACITY — DRY 

1  Ib.  per  bu.— U.  S (0.4536  X  28.378)  =  12.872  kg.  per  stere 

1  Ib.  per  bu.— Gt.  Bt (0.4536  X  27.51)     =  12.479  kg.  per  stere 

PRESSURE 

1  oz.  per  sq.  in (28.35     X  0.155)  =    4.394  g.  per  cm2 

1  Ib.  per  sq.  in (453.59  X  0.155)  =  70.306  g.  per  cm2 

1  Ib.  per  sq.  ft. . . . (0.4536  X  10.764)  =    4.882  kg.  per  m2 


412  MINE  GASES  AND  VENTILATION 

WORK 

1  inch-pound (2.54      X  453.59)       =  1152.1  gram-centimeters 

1  foot-pound (0.3048  X      0.4536)  =  0.1383  kilogram  meters 

1  ton-pound (0-3048  X      0.9072)  =  0.2765  tonne-meters 

WORK  IN  HEAT  UNITS 

1  B.t.u.— 778  ft.-lb (778  X  0.1383)          =  107. 564  kg.-m. 

1  pound-calorie (107.564  X  1.8)         =  193.615  kg.-m. 

1  calorie (193.615  X  2.2046)  =  426.844  kg.-m. 

CALORIFIC  OR  HEATING  VALUE 

1  B.t.u.  per  Ib (0.252  X  2.2046)     =  0.55556  cal.  per  kg. 

1  B.t.u.  per  Ib 5/9(2 . 2046)  =  1 . 22478  Ib.-cal.  per  kg. 

1  B.t.u.  per  cu.  ft (0.252  X  35.3145)  =  8.89925  cal.  per  m3 

1  Ib.-cal.  per  Ib (0 . 4536  X  2 . 2046)  =  1 . 00000  cal.  per  kg. 

1  Ib.-cal.  per  Ib =  2.20462  Ib.-cal.  per  kg. 

1  Ib.-cal.  per  cu.  ft (0.4536  X  35.3145)  =  16.01866  cal.  per  m3 

POWER 

The  metric  horsepower  (force  de  cheval),  which  for  convenience  may 
be  abbreviated  "cheval,"  is  the  power  capable  of  performing  75  kg.-m.  of 
work  per  second,  or  75  X  60  =  4500  kg.-m.  per  min. 

1  horsepower (33,000  X  0.1383)  =  4563.9  kg.-m.  per  min. 

1  horsepower (4563 . 9  -r-  4500)     =  1 . 0142  chevals 

1  cheval (4500  H-  4563.9)     =  0.986  hp. 

POWER  FACTORS 

1  sq.  ft.  per  hp (0 . 093  X  0 . 986)  =  0 . 0937  m2  per  cheval 

1  cu.  ft.  per  hp (0. 028  X  0. 986)  =  0. 0276  m3  per  cheval 

FUEL  OR  WATER  CONSUMPTION 

1  Ib.  per  hp.-hr (0 . 4536  X 0 . 986)  =  0 . 4472  kg.  per  cheval-hr. 

1  ton  per  hp.-hr (0 . 9072  X  0 . 986)  =  0 . 8945  tonnes  per  cheval-hr. 

1  gal.  (U.  S.)  per  hp.-hr .  .  (3 . 785  XO .  986)     =  3 . 7320  liters  per  cheval-hr. 
1  gal.  (Gt.  Bt.)  per  hp.-hr.  (4 . 544  X 0 . 986)     =  4 . 4804  liters  per  cheval-hr. 

EVAPORATION  FACTORS 

1  gal.  per  sq.  ft.— U.  S (3.785  X  10.764)  =  40.7417  1.  per  m.2 

1  gal.  per  Ib.  fuel (3. 785  X    2. 2046)  =    8. 3444  1.  per  kg. 

1  gal.  per  B.t.u (3.785  X    3.968)  =  15.0189  1.  per  cal. 

1  gal.  per  B.t.u (3.785X1.8)  =    6.8130  1.  per  Ib.-cal. 

1  gal.  per  sq.  ft.— Gt.  Bt (4 . 544  X  10 . 764)  =  48 . 91 16  1.  per  m2 

1  gal.  per  Ib.  fuel (4.544  X  2.2046)  =  10.0177  1.  per  kg. 

1  gal.  per  B.t.u (4.544  X  3.968)  =  18.0306  1.  per  cal. 

1  gal.  per  B.t.u (4.544  X  1.8)  =    8. 1792  1.  per  Ib.-cal 


DENOMINATE  NUMBERS  413 

EQUIVALENTS  IN  AIR  MEASUREMENTS 
Atmospheric  pressure,  sea,  level,  normal,  14.696  Ib.  per  sq.  in. 

(14 . 696  X  0 . 0703)  =  1 . 033  kg.  per  cm2 
(14.696  -7-0.4911)  =  29. 925  in.  mercury 
(29.925  X  25.4)  =  760  mm.  mercury 

/29.925  X  13.  6\  ,0  ft  ,, 

I — j       =  33.9  ft.  water  column 

(33.915  X  0.3048  =  10.34m.  water  column 

The  specific  gravity  of  mercury  (32  deg.  F.)  being  13.593,  1  in.  ba- 
rometer (standard  reading)  corresponds  to  13.6  in.  water  gage  and, 
roughly,  to  (13.6  X  815)  -t-  12  =  say  900  ft.  air-column. 


Pressure,  in  fan  ventilation  is  frequently  expressed  in  ounces  per 
square  inch,  instead  of  in  pounds  per  square  inch.  The  following  table 
giving  the  equivalent  values  in  these  denominations  and  inches  of  water 
gage. 

Water  Lb.  per  Oz.  per  Water  Lb.  per  Oz.per 

gage  sq.  ft.  sq.  in.  Gage  sq.  in.  sq.  in. 

0  3  15.60  1.733 

H  0.65  0.072  y±  16.90  1.878 

K  1-30  0.144  Y2  18.20  2.022 

H  1.95  0.216  Y±  19.50  2.167 

H  2.60  0.289  4  20.80  2.311 

%  3.25  0.361  y±  22.10  2.456 

%  3.90  0.433  Y2  23.40  2.600 

%  4.55  0,505  %  24.70  .2.744 

1  5.20  0.578  5  26.00  2.889 
H  6-50  0-722  y±  27.30  3.033 
%  7.80  0.867  %  28.60  3.178 
%  9.10  1.011  %  29.90  3.322 

2  10.40  1.156  6  31.20  3.467 
y±  11.70  1.300                 K  32.50  3.611 
%  .           13.00  1.444                  y2  33.80  3.756 
%  14.30  1.589                 %  35.10  3.900 

The  table  on  the  following  page  will  be  found  convenient  in  comparing 
short  and  long  tons.  It  expresses  the  decimal  equivalent  of  the  short  and 
long  ton,  per  hundredweight,  to  20,000  Ib.  or  10  short  tons. 


414  MINE  GASES  AND  VENTILATION 

TABLE  OF  COMPARATIVE  VALUES  OF  THE  SHORT  AND  LONG  TON 


POUNDS^ 


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INDEX 


NOTE. — Numbers  refer  to  pages.  Letters  are  used  to  abbreviate  words  in  the  same 
line  or  in  the  heading  in  which  they  stand.  Other  abbreviations  are  those  in  common 
use. 


Absolute  pressure,  192 

A.  temperature;  A,  zero,  18 
Rel.  of  a.  p.  to  a.  temp.,  20 
Acceleration,  26   . 
Acetylene  gas,  Generation  of, 

Burning    a.    g. ;    Oxygen  con- 
sumed;   Calculation,    310 
Chem.  reactions,  309 
Properties  of  a.  g.,  311 
Acetylene  lamp   (See  L.,    Miners' 

Carbide) 

Acids,  Bases,  Salts:  Nature  of  a.; 
Distinguishing  character- 
istics, 61 

Affinity  of  atoms,  59 
Afterdamp:  Composition,  etc.,  Ill 
Air,  1  (See  Respiration) 

Composition    of    a.,    4;    Per- 
centage c.  calculated,  30 
Density  of  a.   calculated,   30 
Dry  a.,   4,   70;   Formulas,   4, 

79,  80 
Dry  a,   vs.   wet    a.,    79    (Sec 

Hygrometry) 
Early  theories  of  a.,  1 
Mechanical  mixture,  2,  61 
Moisture  in  a.   (See  Hygrom- 
etry) 

Normal  a.,  4,  5;  Exhaled  a.,  3; 
Free  a.,   19;  Residual  a., 
Tidal  a.,  133 
Weight    of    a.:  Formulas     4, 

79,  80 

Weight  of  a.:  Dif.  altitudes 

and  temp,  (tables)  11,  15 

Air     bridges:  Overcasts;     Under- 

casts;     Natural    o.,     251 

Air  crossings,  249 


Air     columns — Atmospheric     (See 
Atmos.  pressure) 

Average  temp,  (atmos.  a.  c.) 
Calc.    of,     14;    Observed 
temp.  Table  of,  15 
Air  columns,  in  mines: 

Estimation  of,  166;  Condi- 
tions affecting;  Positive 
and  negative  a.c.,  167; 
Downcast,  Upcast  c.  168; 
Calculation  of  a.  c.;  Ef- 
fective depth,  169;  Prob- 
lems, 170;  Relation  of 
a.  c.  to  unit  ventilating 
press.,  184;  Wwater  gage, 
184;  Barom,  pres.,  185 
Air  currents,  Conducting,  249 
(See  Mine  Ventilation) 

Appliances  used:  Air  bridges 
(overcasts  undercasts), 
brattices,  doors,  stop- 
pings, regulators,  249-251 

Circulating  system :  Intake 
and  discharge  openings, 
161;  Intake  and  return 
airways,  258;  Coursing 
the  a.;  Single  current  not 
adequate,  218  - 

Distribution    of    a.,    257;    A. 

splits,  258 

Measurement  of  a.  c.,  199 
Splitting   the  a.   c.  (See   S.   the 
A.  C.) 

Velocity  of  a.  c.,  173,  Danger 
of  high  v.,  179;  How  v. 
is  estimated  and  meas- 
ured, 180;  Rel.  of  pres. 
and  v.,  173 


415 


416 


INDEX 


Air  splits,  258  (See  Splitting  of  the 

A.  Current) 
Airways : 

Definition  of  a.,    187;  Essen- 
tial features;  Shape,   188 
Intake    and    return    a.,     258 
Potential  of  a.,  200;  Table,  202 
Similar   a.,    189,    Principle   of 
s.     a.,     191;     Rule,     192 
Systems  of  mine  a.,  262 
Resistance     of     a.;     How     r. 
varies,    191;    Unit    of    r. ; 
Coef.    of    fric.;    Calcula- 
tion of  r.  of  an  a.,   192; 
Formulas  for  r.  196,  198 
Anemometer,  The,  180 
Artificial  respiration  (See  R.) 

Sylvester  method,  158;  Schae- 

fer  method,  159 

Ashworth-Hepplewhite-Gray  safe- 
ty lamp,  283 

Atmosphere,  The,  5  (See  Air) 
Constant  composition,  61 
Pressure  expressed  in  a's,  19 
Atmospheric  pressure,  5 

A.  p.  at  dif.  altitudes,  Table  of, 
11;  Relation  of  a.  p.  to 
altitude,  temp.,  etc.,  Table 

of,  15 
Calculating  a.  p.  (Differential 

method),  15 

Measurement    of    (See    Baro- 
metric Pressure) 
Variation  of,  Daily  and  yearly, 

6 

Atoms,  corpuscles,  electrons,  mole- 
cules, 22 

Atomic  heat,  re  a.  wt.,  53 
Atomic   volume,   unit   of   gaseous 

v.,  29,  63 

Atomic  weight,  rel.  w.,  59;  A.  w. 

of    elements    (table),    28 

Attraction,  Law  of,  22,  Terrestrial 

a.,  23 

Authorities:  Abel,   122;  Atkinson, 
191;        Avogadro,        29; 


Beard,  305;  Berzelius, 
122;  Boyle,  19;  Burrell, 
296;  Cavendish,  1;  Cham- 
berlin,  90;  Charles,  18; 
Clowes,  311;  Dalton,  22; 
Davy,  269;  Dulong,  53; 
Emich,  113;  Fairley,  191; 
Favre,  66,  68;  Galloway, 
304,  305;  Gay  Lussac, 
18;  Gibbs,  143;  Graham, 
37;  Haldane,  106,  107, 
109;  Hopkins,  157;  Lav- 
oisier, 1 ;  LeChatelier,  114, 
311;  Mallard,  114;  Man- 
ning, 157;  Mariotte,  19; 
Paul,  147;  Petit,  53; 
Priestley,  1;  Remsen,  53; 
Schaefer,  159;  Silber- 
mann,  66,  68;  Stephen- 
son,  268;  Stewart,  134; 
Stoney,  22 ;  Sylvester,  158; 
Taffanel,  123;  Thomson, 
22 

Avogadro's    law    of    gaseous    vol- 
ume, 29 


B 


Barometer,  The,  6 
Aneroid  b.,  9 
Mercurial  b.,  6;  Description, 

8;  Principle  of  b.,  7 
Barometric  pressure,   6    (See   At- 
mospheric P.) 

Calculation  of  p.  from  b. 
reading  6;  Calculation  for 
any  altitude,  12;  Form- 
ula, 13 

Standard,  b.  readings,  8 
Table  of  b.  p.  at  dif.  altitudes, 

11 

Bases,  in  chemistry,  61 
Battery,  Edison  storage,  313 
Beard-Mackie       sight      indicator, 
for  gas,  297 


INDEX 


417 


Birds,  Effect  of  carbon  monoxide 
on,  106;  Table  showing 
length  of  exposure  and 
recovery,  108 

Blackdamp,  110  (See  Carbon  Diox- 
ide) 

Carbide  lamps  in  b.,  311 
Definition;       Production       in 
mines;  Effect  on  human 
system,  110 

Blood,  Circulation  of,  3  (See  Respi- 
ration) 

Absorption  of  carbon  mono- 
oxide    by    the    b.,     103; 
Rate  of  a.,  104 
B.  test  for  carbon  monoxide, 

106 

Percentage    of    saturation    in 
b.  re  p.  c.  in  air  breathed, 
105;  P.    of   carbon   mon- 
oxide fatal  to  life,  107 
Blowers,  Gas,  87  (See  Geological 

Conditions) 

Blownout  shot,  cause  of  mine  ex- 
plosion, 127 

Boiling,  Evaporation,  Vaporiza- 
tion, 50 

B.  points  of  dif.  liquids,  Table, 
51;    Effect  of    pres.    on 
b.  p.  and  v.,  50 
Bonnet,       Lamp       (See   L.    Mine 

Safety) 
Box     regulator,     The,     231     (See 

Regulators) 
Area    of     opening,   Example, 

234,  240 

Pres.  due  to  b.  r.,  232 
Brattices,    249;    How    built,    250 
Breathing     Apparatus,     132     (See 

Respiration) 

Design;      Development,      135 
Permissible  b.  a.;  Definition, 

148 

.  Principle  of  b.  a.,  132 
Regenerator,  136 
Specifications  by  the  Bureau 

27 


of  Mines:  Conditions 
of  testing,  148;  Character 
of  tests,  150;  Construc- 
tion of  b.  a.,  151;  Detail 
of  procedure  in  tests, 
153;  Approval  of  a.,  155 
Notification  to  manufac- 
turer; Fees  for  testing; 
Application  for  test  of  a., 
156 

Testing  b.  a.,  136 
Types  of  b.  a.,  137: 

Draeger  b.a.,  137;  Essen- 
tial parts;  Capacity,  139 
Fleus  Proto  b.  a.,  139; 
Essential  parts,  140;  Ca- 
pacity, 142 

Gibbs  b.  a.,    143;  Circu- 
lation, 144;  Testing  145 
Paul  b.  a.,  147 
British  thermal  unit,  51 
Burrell  gas  detector,  The,  299 
Bureau  of  Mines,  147 

Requirements  in  breathing 
apparatus,  147;  Specifica- 
tions b.  a,  148;  Electric 
mine  lamps,  319;  Mine 
safety  lamps,  288 

C 

Calorie,  52 

Pound,     c.,     52;     Equivalent 

B.t.u.,  etc.,  53 
Canary,  (See  Birds  etc.) 
Cap,  Flame, (  See  F.  C.) 
Cap  lamp,  Electric,  (See  E.  Mine 

L.) 

Carbide  lamps  (SeeL.  Acetylene  C.) 
Carbon,    Heat   of   combustion   of, 

66 

Thermochemical  equation,  69 
Carbon  dioxide,  109 

Absorption    of,   in    breathing 

apparatus,  136 

Amount  produced  in  breath- 
ing, 134 


418 


INDEX 


Carbon  dioxide,  Effect  on  flame; 
on  life;  on  respiration; 
Production  in  mines,  109 

Reduces  poisonous  effect  of 
carbon  monoxide,  107 

Toxic  effect,  2,  109,  312 

Treatment  of  victims,  110 
Carbonic    acid    gas    (See    Carbon 

Dioxide) 
Carbon  monoxide,  103 

Absorption  by  blood  103; 
Rate  of  a.;  Fatal  per- 
centage, 1G4 

Combustion  in  air  (chem. 
equa.),  65 

Detection  in  air;  Blood  test, 
106 

Effect  on  birds  and  mice;  on 
flame,  106;  on  life,  103; 
Haldane's  conclusions, 
107 

Explosive  and  inflammable 
range  (table) ;  Effect  of 
high  press,  and  temp., 
114;  Moisture  necessary, 
114,  121 

Flame  temp.,  Calculation  of, 
120 

Production  in  mines,  105 

Properties,  103 

Treatment  for  c.  m.  poisoning, 

103 

Catalysis,  122 

Centigrade  re  Fahrenheit  scale 
(table),  44 

Conversion  formulas;  Ex- 
amples, 45 

Charts:  Explosive  mine  gases; 
E.  range;  Max.  e.  point; 
Inflammable  limits; 
Symbols;  Molecular  wts., 
Densities;  Wt.  per  cu.  ft.; 
Vol.  per  pound;  Specific 
heats;  Heat  of  combustion 
in  oxygen ;  Chem.  equation 
showing  reaction,  115 


Flame  caps  in  safety  lamps; 
Height  of  f.  cap  or  elon- 
gation of  f.  for  dif.  illumi- 
nants  and  dif.  percentages 
of  gas;  Inflammable  and 
explosive  zones,  303 

Humidity  of  air  for  dif. 
dry-and-wet  bulb  read- 
ings; Percentage  and 
weight  of  water  vapor  in 
air,  81;  Table,  75 

Pressure  (atmospheric)  at  dif. 
altitudes;  Corresponding 
water  column  and  baro- 
meter; Mean  observed 
temp,  of  atmosphere,  15 

Pressure,  power,  volume:  Lb. 
p.  sq.  ft.;  Oz.  p.  sq.  in.; 
water  gage,  inches,  184 

Temperature :  Expansion 

curve  for  air  and  gases; 
Relation    of    absolute    t. 
and  volume,  19 
Chemical  affinity,  46,  56 

C.    change;   C.    reaction,    56, 
62;  Examples  of  c.r.;  Effect 
of  heat  57;  C.  compound, 
60;    C.    equation;    How 
written,     62;      What     it 
shows,  67;   Use  of  c.  e., 
63;  C.  symbols,  58 
Chemistry  of  gases,  56 
Chesneau  safety  lamp,  283 
Chokedamp,     109     (See     Carbon 

Dioxide) 

Circulation  in  mines  (See  M.  Venti- 
lation) 

Flow  of  air  in  airways,  172; 
Potential  of  c.,  201;  P. 
values  for  dif.  c.,  202; 
Table,  203;  Pres.  pro- 
ducing c.,  174;  Power 
required  to  produce  a 
given  c.,  249 

Tandem  c.;  Summation  of 
potentials,  214;  Formulas, 


INDEX 


419 


215;  Examples  int.  c.,  216, 
237;  T.  vs.  split  c.,   222 

Circulation  of  blood,  3  (See  B.,  C.  of) 

Clanny  safety  lamp,  277 

Clowes  hydrogen  safety  lamp,  284 

Coal:  Condition  of  gas  in  c. ; 
Escape  of  g.  from  c. ; 
Gas  evolved  from  c.  in 
vacuum,  90;  Heat  value 
of  some  coals  (table),  66; 
Inflammability  of  c.,  124 

Coal  dust,  123  (See  D.,  C.) 

Coefficient  of  friction  of  air: 
Atkinson  c;  Fairley  c., 
192 

Cohesion,  22 

Combustion:  A  form  of  oxidation; 
Products  of  C. ;  Slow  c.; 
Supporter  of  c.,  57 
Heat  of  c.  (exothermic) ; 
Formula;  Table  of  h.  of 
c'.,  66;  Calculation  of  h. 
of  c.,  67 

Rapid  (active)  c. ;  Spontaneous 
c.,  58 

Composition,  Percentage :  By  vol- 
ume, 40;  By  weight,  39 

Conducting  air  currents,  249  (See 
A.  C.,  C.) 

Conduction  of  heat,  52 

Convection,  52 

Conversion  formulas:  Degrees  of 
temp.,  45;  Heat  units,  52 

Conversion   tables,    406    (See    T.) 

Corpuscles,  22 

Critical  temp,  of  a  liquid,  81 

D 

Damps,  94 

Davy  safety  lamp,  The,  275 
Deliquescent,  48 
Denominate  numbers,  397 
Density     defined;     Formula,     29 
Calculation  of  d.  from  relative 

(atomic)  wts.,  30 
Mass,  volume,  d.,  24 


Dew  point,  5,  76 

D.  p.  temp.,  76 

Diffusion  of  ah-  and  gases  34,  36 
Law  of   d.,  36;  Graham's  1.; 
Illustration ;  Experiment, 
37.;  Calculation  of  den- 
sity based  on   1.  of    dif- 
fusion; Formula,  41 
Dip  workings,  Ventilation  of,  162 
Distribution  of  air  in  mines,  257 
Division  of  air:  (See  Splitting  the 

A.  Current) 
Natural  d.  220;  Proportionate 

d.  230 
Door  regulator,  The,  231; 

Area  of  opening;  Use  of  the 
d.  r.,  235;  Example,  240 
Doors,  Mine,  249 
Double -entry  system,  263 
Draeger  breathing  apparatus,  137 
Drainage,  Mine  252 
Dust,  Coal,  123  (See  D.  Explosion) 
Anthracite  d.,  124 
Effect  of  c.  d.  on.  flame,  123 
Inflammability  of  c.   d.,    124 
Dust,  Shale  or  Stone, 

Barrier     to     propagation     of 

explosion,  125 

Catalytic  action  of  s.  d.,  122 
Dust  explosion,  116  (See  E.,  D.) 
Dynamic  force,  25 

E 

Edison   storage   battery  for  mine 

lamps,  313 

Electric    mine    lamps,     128,    313 
(See  Incandescent  L.) 

Battery,  Selecting  a  suitable; 
Edison  storage  b.,  313; 
Charging  the  b.,  315; 
Cap  1.  and  cable,  314 

Permissible  e.  m.  1.;  Defini- 
tion, 319 

Specifications  (Bureau  of 
Mines) ;  Conditions  of 
testing,  319;  Require- 


420 


INDEX 


ments       for       approval, 
320;      Tests     of     design . 

and    construction; 

safety       devices,       323; 

short    circuit ; 

— lighting   324; cur- 
rent consumption,  candle 

power,  life  of  bulb; 

— leakage  of  electrolyte; 
Approval,  325;  Notifica- 
tion of  manufacturer; 
Fees  for  testing,  326 
Use  of  e.m.l.,  317 

Electric     wires,     switches,     fuses, 
brushes,  sparking  of,  127 
Electrons,  22 
Elements,  The,  28 

Classification    of    the    e.,    60 
Combining    power;     Valence, 

59 
Heat  of  e. ;  in  reaction,  always 

zero,  65 

Emission  of  gases,  34  (See  Trans- 
piration of  G.) 
Endothermic  reaction,  65,  67 
Energy:  Definition;   Forms   of  e; 
Kinetic  e.J   Potential   e., 
27;  Heat  e.    never   lost, 
67 

Equations:  Chemical  e.,  62;  Ther- 
mochemical  e.,  67;  E.  of 
time,  402 
Ethane,      89;      Occurrence      and 

properties,  92 
Ethene    (ethylene),    89    (See  Ole- 

fiant  Gas) 

Equivalents  hi  measurement,  184 

Air    column    re    water    gage; 

re    unit    of   vent,    pres., 

184;  re  barometric  pres., 

185 

Atmospheric  pressure  e.,  413 

Barometric    pressure    re    air 

column;  re  unit  of  vent. 

pres.,  185 

Power,  volume  (diagram),  185 
Pressure  e.  (table),  185 


Evaporation,   50    (See   Boiling,    E. 

etc.) 

Exothermic  reaction,  65,  67 
Expansion  of  air  and  gas ;  17 

Adiabatic  e. ;  Formulas,  21; 
Isothermal  e.,  22 

Coefficient  of  e.  or  contraction, 
17 

Effect  of  press,  and  temp.,  17; 
Addition  of  heat,  20 

Pressure  re  abs.  temp.,  20; 
re  volume  (Boyle's  or 
Mariotte's  law),  19 

Temperature  (absolute)  re 
volume  (Charles'  or  Gay 
Lussac's  law),  18 

Volume,  press.,  abs.  temp., 
Rel.  of;  Formulas,  20 

Work  of  e.,  calculated  in  two 

ways,  20,  21 
Explosion,  Dust,  116: 

Absence  of  gas;  Character  of 
d.;  Influence  of  d.  on  e.; 
Pioneering  cloud  of  d. ; 
Weight  of  d.  per  cu.  ft.  of 
air  to  render  air  explosive, 
123;  Inflammability  of 
coal  d.,  124 

Anthracite  d.  not  explosive; 
Volatile  combustible  mat- 
ter in  coal  an  index  of  its 
explosibility,  124 

Incombustible  d,  Influence 
of,  125  (See  D.,  Shale  or 
Stone) 

Explosion,  Gas  (See  Mine  Gases; 
E.,  Mine) 

Definition  of  g.  e.,  116 

E.  of  g.;  Influence  of  pres. 
and  temp,  on  e.,  121;  I.  of 
catalysis,  initial  impulse, 
moisture,  volume  and  in- 
tensity of  flame,  122;  I.  of 
coal  dust  on  e.,  123;  I.  of 
rock  dust  to  arrest  e.,  125 

Peculiarities  of  e.  of  methane, 
114 


INDEX 


421 


Explosion,    Mine,     126     (See    E., 

Dust;  E.,  Gas) 
Causes  of  m.  e.,  127 
Definition  of  a  m.  e.,  116 
Development   of  the   e.,    126 
Propagation  of  an  e.  in  a  m.; 

Pioneering  cloud,  123 
Prevention  of  m.  e.,  129;  Shale 

or   stone    dust    (See    D., 

S.  or  S.) 

Rescue    and    first-aid    work; 
Entering  a.  m.  after  an  e., 

131; 
F-a.   suggestions,    132    (See 

F-A.  W.;  Breathing  Ap- 
paratus) 
Explosive   Mine   Gases,    112,    115 

(See   M.    G.;   Firedamp) 
Chart  showing  e.  range,  etc. 

of  m.  g.,  115 
Effect  of  high  pres.  and  temp. 

on  e.  range,  114 
E.    and    inflammable    limits; 

E.  range  of  g. ;  Maximum 

e.  point ;  Lower  and  higher 

limits;    Degree  of  explo- 

siveness,     how     affected, 

113;  Table,  114 
Inflammation  of  gas;   Theory 

of,  116  (See  Inflammable 

M.  G.) 


Fahrenheit  scale,  43 

F.  re  centigrade,  s.  (table), 
44;  Conversion  formulas; 
Examples,  45 

Faults  in  mining  (See  Geological 
Conditions) 

Feeders,  Gas;  Blowers,  87;  Com- 
position of  f.  g.,  91;  Oc- 
currence, 87 

Federal  Bureau  of  Mines  (See 
B.  of  M.) 

Firedamp,  94 

Definition,  94 


Firedamp,  Effect  of  dust  and  other 
gases,  95 

F.  is  a  mechanical  mixture,  38 

Inflammable  and  explosive 
range,  Table  of,  101; 
Lower  i.  limit,  95;  Cal- 
culating the  1.  i.  1.,  96; 
Percentage  of  gas,  98;  L. 
e.  limit;  Max.  e.  point, 
98;  Percentage  of  gas,  99; 
Higher  e.  limit,  99;  Per- 
centage of  gas,  100;  High- 
er i.  limit,  100 

Fitst-aid  work,  157  (See  Artificial 
Respiration;  Breathing 
Apparatus) 

Resuscitation,  157 

Suggestions    on    f.— a.    to    ex- 
plosion victims,  132 
Flame,  Nature  and  temperature  of, 
117 

Effect  of  coal  dust  on  f.,  123;  E. 
of  carbon  dioxide  on  f . ,  109 ; 
E.  of  c.  monoxide  on  f .,  106 

Extinction  of  lamp  f.  in  car- 
bon dioxide,  109;  E.  of 
carbide  f .  by  depletion  of 
oxygen,  312 

Kinds  of  f. :  Gas-fed  f.;  Oil-fed 
f.,  109,  312 

Lamp  f.,  Chart  of,  303 

Temp,  of  f.,  Theoretical;  Cal- 
culation   of    f.    t.,    118; 
Methane     in     air,     119; 
Carbon  monoxide  in  air, 
120;    Temp,  of  f.  re 
temp,  of  ignition  of 
gas,  118 

Volatile-oil  f .  sensitive  to  gas, 
288 

Volume  of  f.,  Estimated,  121 

Zones  inf.,  118,301 
Flame  caps:  Fuel  c.;  Gas  c.,  302 

Calculation  of  height  of  f.  c. 
304;  Formulas,  305 

Chart  of  f.  c.,  303 


422 


INDEX 


Flame  caps :  Height  of  f .%  c.  re 
percentage  of  gas,  303, 
305 

Flame  test,  The,  301  (See  Testing 
for  Gas) 

Flashdamp:  Definition;  Calcula- 
tion of  composition  of 
f.,  101;  Percentage  com- 
position, 102 

Fleuss  Proto  Breathing  Apparatus, 
139 

Flow  of  air  in  airways,   172  (See 
Air     Currents,  ;  Conduct- 
ing; Airways). 
Appliances  for  conducting  the 

a.,  249 

Coefficients  of  friction :  Atkin- 
son jFairley,  192 
Pressure    producing     circula- 
tion, 174;  Power  required 
to  produce  c.,  249 
Resistance     of     a.;     How     r. 
varies,    191;    Unit   of   r., 
192 

Fluid  ounce,  The,  405 

Fluid  state,  23 

Force:  Measurement  of  f.;  Static 
f.;  Dynamic  f.,  25 

Formulas  and  symbols,  192 

Basal  f . ;  Important  principles, 

196 

How  factors  vary,  195 
Use  of  f.,  194;  Illustration  of 
f.,  197 

Free  air,  19 

Free  split,  233 

Freezing  points  of  liquids  (table),  51 

Difference  bet,    melting    and 

f.  p.;  Effect  of  pres.,  49 

French  thermal  unit,  52 

Friction,  Coefficient  of;  Atkinson  c. ; 
Fairley  c.,  192 

Fuel  cap  in  testing  for  gas,  302 

Furnace  ventilation;  Principle  of 
f.  v.;  Location  of  a  mine 
furnace;  Construction  of 


f.,    164;    Area    of    grate; 
Wt.   of   coal   burned   per 
hr.,  165;    Formula;    Ex- 
ample, 166 
Fusion,  Heat  of,  48;  Table  of  h. 

of  f.,  50 
Effect  of  pressure  on  f .,  49 


G 


Gas  cap,  in  testing  for  g.,  302  (See 

Flame  C.) 

Gases,  23  (See  Mine  G.;  Geologi- 
cal conditions) 

Blower  g.,  87  (See  Feeder  G.) 

Composition  of  g. ;  Simple  or 
elementary;  Compound, 
38 

Density,  Standard  for  g.,   31 

Expansion  and  contraction  of 
g.;  Coef.  of  e.  or  c. 
17 

Gaseous  state,  23;  Distribu- 
tion of  heat  by  convection 
in,  g.,  52 

Hydrocarbon  g.  (See   H.  G.) 

Natural  g.,  87; 

Gases,  Olefines;  Paraffins,  92  (See 
Hydrocarbon  Gases) 

Vapors  and  g.,  Difference,  24 
Gas  explosion,    116    (See  E.,    G.) 
Gas  feeders,  87  (See  F.,  G.;  Geo- 
logical conditions) 
Gas  indicators,  296;  Beard-Mack- 
ie,     297;     Burrell,     299; 
Liveing,  296 
Geological  conditions,  86 

Condition  of  gas  in  coal;  Es- 
cape of  g. ;  Composition 
of  g.  evolved,  90 

Effect  of  faults,  87 

Gas  feeders,  Blowers,  87; 
Composition  of  f.  g. 
(table),  91 

Gas,  oil  and  water  in  the 
strata,  86 


INDEX 


423 


Geological      conditions,      Natural 

gas,  87 
Occluded    gases;    Pressure   of 

o.  g.,  35,  88 
Outbursts  of  gas,  88 
Water  level  in  strata,  87 
Gibbs    breathing    apparatus,    143 
Gram-atom,    53;     G. -calorie,     67; 

G.-molecule,  47,  54 
Gravitation :  Gravity,  23 

H 

Haemoglobin  or  red  corpuscles  of 
the  blood,  3;  Affinity  of 
h.  for  carbon  monoxide, 
103 

Haulage,  as  affecting  plan  of  mine, 
253 

Direction    of   road   for   given 
grade;  inclined  seam ;  Rule 
and  formula,  254 
Heat,  42 

Definition;  Theory  of  h.; 
H.  in  bodies,  42;  Ab- 
sorption of  h.,  47;  Dis- 
appearance of  h.;  Total 
h.  in  a  body,  48;  H.  cal- 
culation, 67;  H.  changes; 
H.  of  decomposition; 
H.  of  elements,  H.  of 
formation  or  combi- 
nation, 65;  H.  of  fusion; 
h.  of  vaporization;  H.  of 
condensation,  48;  H.  of 
reaction,  positive  h.,  nega- 
tive h.,  67 

H.  energy,  20;  No  h.  e.  lost, 
67;  Transformation  of  h. 
e.,  47 

H.  re  temp.,  43;  Sensible  h.; 
Latent  h.,  46 

Kinds  of  h. :  Atomic  h.,  53; 
Chemical  h. ;  Molecular 
h.,  46; 

Combining  h. ;  H.  due  to  fric- 
tion, impact,  pressure,  47; 


Heat,  H.  of  combustion,  66;  Spe- 
cific h.  or  relative  h.  ca- 
pacity, 54 

Measurement  of  h.,  51  (See 
M.  of  H.) 

Mechanical  equivalent  of  .h, 
53 

Sources  of  h.,  46 

Tables:  H.  of  combustion,  66; 
H.  of  formation  or  com- 
bination, 68;  H.  of  fusion, 
50 

Specific  h.,  solids  and  liq- 
uids; S.  h.,  gases  and 
vapors,  55 

Transmission  of  h.;  Radia- 
tion ;  conduction ;  con- 
vection. 52 

Units    of  h.,  51;    Conversion 
formulas,    52;    Definition 
of  a  u.  of  h.,  54 
Horsepower  in   mine  ventilation: 

Calculation  of  h.  from  mine 
potential,  207,  212,  213; 
C.  of  h.  in  natural  division 
of  air,  227;  Proportionate 
div.  of  air,  232;  secondary 
splitting,  239 

Humidity    (Relative)    of    air,    74; 
How  measured  71;  Tables, 

75,  81 

Hydrocarbon  gases,  91;  Acety- 
lenes; Olefines;  Paraffins, 
92 

General  formulas  for  h.  g., 
91 

Heavy  h.  g.;  Ethane;  Ethene, 
ethylene  or  olefiant  g. 
92 

Light  carbureted  hydrogen, 
methane,  92 

Occurrence  and  formation,  92 

Hydrogen:       Symbol,     mol.    wt., 

density,  sp.  gr.  (table)  89 

Explosive  range,  Inflammable 
limits  (table)  114 


424 


INDEX 


Hygrometer,  The  (Psychrometer) , 
71 

Indicates  degree  of  saturation 
of  air,  74 

Principle  of  the  h.,  73 

Swing  p.,  73 

Wet-and-dry-bulb  h.,  72 
Hygrometry,  70 

Calculation  of  wt.  of  moisture 
in  air,  70;  Formulas,  79, 
80;  Caution,  78 

Dew  point,  The,  76 

Dry  vs.  wet  air,  Deg.  of 
saturation,  70  D.  and 
w.  a  compared,  79;  For- 
mulas, 79,  80 

Humidity  (Relative)  of  air, 
74;  How  measured,  71 

Tables,  75,  81 

Vapor  pressure,  Actual;  How 
calculated,  75;  Saturated 
(table),  77 

Vapors,  Laws  of,  80 


Illuminants  for  safety  lamps,  307 
Light    volatile    oils:  Benzine, 
gasoline,     naphtha,     308 
Mineral  oils:  Crude  petroleum 
(rock    o..),    307;    Coal  o. 
(kerosene),  308 
Incandescent  lamps : 

Cause    of    mine     explosions, 

127 

Conditions   of  breaking,    128 
Indicators,  Gas  (See  G.  1.) 
Inertia,  a  property  of  matter,  23 
Inflammable  and  Explosive  Mine 
Gases,  112,  (See  E.  M.  G.) 
1.  gases,  The,  112;  I.  limits  of 
gases  (table)  114;  range, 
112 

Inflammation  of  gases;  Theory 
of,  116 


Lamp  flames  (chart;,  303 
Lamphouse  or  station,  293 
Lamps,  Acetylene    (Carbide),  308 

(See  A.  Gas) 
C.  1.  in  blackdamp,  311 
Extinction  of  c.  L,  312 
Precautions   in   use   of   c.    1., 

313 
Lamps,    Electric    Mine,   313    (See 

E.  M.  L.) 
Lamps,  Mine  safety, 

Bonnet  or  shield,  271;  Effect 

on  flame  cap,  303 
Chart  of  1.  flames,  303 
Classification  of  s.  1.,  270 
Defective  s.  L,  cause  of  explo- 
sion, 127 
Historical   grouping   of    s.    L, 

286,  287 

Illuminating  power,  273 
Lock     fastenings,     Lead      1.; 

Magnetic  1.,  272 
Oil-burning    1. ;     Non-volatile 

o.;  Volatile  o.,  271 
Permissible  m.   s.   L;    Defini- 
tion, 288 

Principle  of  construction ;  Pro- 
tecting shield ;  Stephen- 
son  L,  268;  Wire  gauze, 
269 

Requirements  of  a  good  test- 
ing 1.;  Sensitive  to  gas, 
270;  R.  of  working  1., 
272 

Specifications  by  the  Bureau 
of  Mines,  274;  Conditions 
of  testing,  288;  Mechani- 
cal tests;  Photometric  t. 
Explosion  t.,  290;  Tests 
of  glasses;  Igniter  t.,  291; 
Approval  of  s.  1.,  292; 
Notification  to  manufac- 
turer; Fees  for  testing, 
293 


INDEX 


425 


Lamps,  Mine  safety: 

Types  of  1.,  Characteristic, 
275:  Davy,  275;  Clanny, 
277;  Marsaut,  278;  Mu- 
eseler,  279 

Types     of    1.,    Special,    281: 
Pieler,     282;     Chesneau; 
Ashworth  -  Hepplewhite- 
Gray,   283;   Stokes   alco- 
hol;    Clowes     hydrogen, 
284,  Wolf,  285;  Miscella- 
neous 1.,  286,  287 
Use  and   care   of  s.   1.,   293; 
Handling    of    s.    1.,    294 
Volume    of   1.    chimney,    269 
Latitude  etc.,  402 
Laws  of  gases : 

Avogadro,     law     of     gaseous 

volume,  29;  Application,  64 

Boyle-Mariotte,    law    of   vol. 

re  pres.,  19 
Charles-Gay    Lussac    law    of 

vol.  re  temp.,  18 
Graham,  law  of  diffusion  of 

air  and  g.,  36,  37 

Liquid  state,  23;  Liquefaction,  48; 
Distribution  of  heat    by 
convection,  in  liquids,  52 
Logarithms : 

Definition;  Systems;  Charac- 
teristic,    Mantissa,    328; 
How  to  find  1.  of  a  number, 
329;     Use     of    1.,     330; 
Rules;    Arithmetical    comple- 
ment,  Antilog.  331;   Ex- 
amples, 332;  Table  of  1. 
333-351 

Lighting,    Mine   lamps    and,   268 
Liveing  gas  indicator,  296 
Longwall  plans,  256,  257 

Ventilation  of  1.  workings,  256 
Longtiude  etc.  402 

M 

Marsant  safety  lamp,  278 
Marsh  gas  (See  Methane) 


Mass,  property  of  matter,  22 

M.,    volume,    density;    Unit 
of    m.,    24;    Measure   of 
force,  25 
Matter,  22 

Definition;    Divisions   of   m.; 

Properties  of  m.,  22 
Heat  a  condition  of  m.,  51 
M.  is  indestructible,  62 
Molecular    theory    of  m.,  59 
Measurement,  25 

Distance;  Force;  Static  f., 
Dynamic  f.;  Formulas, 
25;  Tine;  Special  units 
of  m.;  Compound  units, 
26 
Energy;  Forms  of  e.;  Kinetic 

e.;  Potential  e.  27 
Measurement  of  air  currents,  199 

(See  Mine  Potential) 
Measurement  of  heat,  51 

Standards  of  h.  m.;  Thermal 
units;   British  t.   u.,   51; 
French  t.  u.  or  calorie;  Pound 
c.;  Conversion  formulas, 
52 
Measurement  of  time,  402 

Sun  t.;  Equation  of  t.;  Sid- 
ereal t.;  Local  t. ;  Stand- 
ard t.,  402;  Eastern  t.; 
Central  t.,  Mountain  t., 
Pacific  t.;  Civil  t. ;  Astro- 
nomical t.,  403 
Measurement  of  humidity  (See 

H.  of  Air) 

Measurement,  Relative  (See  Spe- 
cific M.) 
Measures,  Weights  and   (tables), 

397 

U.  S.  and  British  system,  398; 
Metric  system,  403;  Me- 
,  trie    abbrevations;    Con- 
version tables  406;  Com- 
pound units,  411 

Mechanical    equivalent    of    heat, 
53 


426 


INDEX 


Melting  points  of  substances,  49 

Difference  bet.  m.  p.  and 
freezing  p. ;  49 

Table  of  m.  p.  of  substances, 

50 

Mercurial  barometer,  The,  6 
Methane    (Marsh    gas),    93    (See 
Firedamp) 

Combustion  of  m.  in  air  or 
oxygen,  64;  wt.  of  o. 
per  Ib.  of  m.,  96;  Vol. 
of  o.  per  unit  vol.  of 
m.,  64;  Effect  of  other 
gas.es  and  dust,  95;  Heat 
of  c.  of  m.  in  air  (table), 
66;  Heat  of  formation  of 
m.  (table),  68;  Heat  cal- 
culation, 67 

Explosive  limits  of  m.  (table), 
114 

Flame  temp,  of  m.  burning  in 
air,  calculation,  119 

Occurrence  and  properties,  93, 
Occluded  in  coal  forma- 
tions, 88 

Percentage  composition  of  m., 

39 
Mine  air,  5  (See  A.) 

Concussion    of    a.    in    mines, 

127 

Mine   gases,    86    (See    Geological 
Conditions) 

Chart  of  m.  g.,  115 

Common    m.    g.    (table),    89 

Explosive  m.  g.  (see  E.  M.  G.) 

Inflammable  m.  g.  (See  1. 
M.  G.) 

Properties    and    behavior    of 

m.  g.,  93 
Mine  potential,  The,  199  (See  P.) 

Effect  of  splitting  on  m.  p., 
203,  Illustration,  204  ; 
Practical  example,  205; 
Examples,  209;  Formu- 
las: M.  power  p.;  M. 
pressure  p.  211 


Mine  potential : 

Formulas:  Power  p.,  197; 
Pressure  p.,  198 

General  m.  p.,  212;  G.  m.  p., 
equal  splits,  213;  G.m.p., 
natural  division  of  air, 
Example,  228 

P.  of  airway,   200;  Table  of 
values,  dif.  a.,  202;    P.  of 
circulation,  201 ;  Table  of 
values,  dif.  c.,  203 
Mineral  oil,  307 

Mine -rescue  work  and  appliances, 
131   (See  Explosion,   M.) 
Mine  Ventilation,    1G1    (See   Fur- 
nace V.;  V.,  Practical) 

Conducting  air  currents  in 
mines  (See  A.  C.,  C.) 

Formulas,  197-199;  Basal  f., 
196 

Kinds  of  v.;  Natural  v.; 
Slope  and  dip  workings, 
162 

Power  on  the  air;  Work  and 
p.  synonymous,  182;  P.- 
press.-vol.  chart,  185;  P. 
formulas,  199;  P.,  press., 
quantity,  201 

Pressure,  Ventilating,  174:  P. 
producing  circulation;  P. 
how  produced,  174;  P. 
how  estimated;  P.  how 
measured,  175;  P.  formu- 
las, 198;  unit  of  v.  p., 
177;  P.  calculated  from 
m.  potential,  206;  P. 
due  to  regulator,  232; 
P.  re  velocity;  173; 
Equivalents  in  v.  p.  (table) 
175,  185 

Quantity  of  air,  181:  Q.  of 
a.  required;  Q.  how  esti- 
mated ;  Q.  how  measured, 
181;  Q.  formulas,  198;  Q. 
calculated  from  m.  po- 
tential, 207 


INDEX 


427 


Mine  Ventilation: 

Resistance  of  airways,  191 
(See  A.) 

Requirements  in  v.,  161;  R. 
of  the  m.  law,  182, 
199 

Spitting  air  currents  (See  S.  A. 
C.; 

Symbols  and  formulas,  192 

Systems  of  v.,  261 :  Blowing 
s.,  174,  262;  Exhaust  s., 
174,  261;  E.  vs.  B.  s.  of 
v.,  261 

Variation  of  factors,  247 
Mixed  lights  in  mines,  127 
Molecular  state,  23 

M.  forces:  M.  attraction;  M. 
repulsion,    23;    M.   heat, 
46;  M.  h.  of  reaction,  67; 
M.  theory,  59;  M.  volume, 
29;  M.  weight,  59 
Molecule,  The. — Definition,  Sym- 
bol; Atoms  in  a  m.,  58 
Mueseler  safety  lamp,  279 

English  and  Belgian  types, 
280 

N 

Natural  division  of  air,  220  (See 
Splitting  the  A.  Current) 

Natural  gas,  87 

Natural  overcast,  251 

Nitrogen  in  air:  Percentage  by 
vol.,  by  wt,  (table), 
4;  Rel.  veloc,  of  trans- 
piration from  coal  (table), 
35;  N.  in  blackdamp,  110; 
N.  in  afterdamp,  111; 
Symbol,  mol.  wt.,  den- 
sity, sp.  gr.  (table),  89 

Non-volatile  oils  used  in  safety 
lamps,  307 

O 

Occlusion  of  Gases,  34  (See  Geo- 
logical Conditions) 


Occlusion  of  Gases : 

Examples  of  o.;   Pressure  of 

o.  g.,  35,  88 
Oil -burning  lamps,  271 
Oils:  Non-volatile  o.  used  in  safe- 
ty    lamps ;     Animal    o. ; 
Vegetable  o.,  307 
Mineral  o.  (rock  o.),  307;  Coal 

o.  or  kerosene,  308 
Volatile     o.,     271;     Benzine, 
naphtha,     gasoline,     308 
Water,  gas  and   o.   in  strata, 

86 

Olefiant  gas  (ethene,  ethylene),  92 
Composition,  59 
Density,  sp.  gr.,  mol.  wt.,  sym- 
bol, 89;  Chart,  115 
Inflammable,  112 
Occurrence  and  properties,  92 
Rel.  rate  of  transpiration,  35 
Olefines,  92 

Open  lights  cause  of  explosion,  127 
Open-flame  lamp,  (carbide  1.),  308 
Ounce,  The  fluid,  405 
Outbursts  of  gas,  88 
Overcasts,  249,  250,  251 
Oxides:  Monoxide;  Dioxide;  Tri- 

oxide,  62 
O.  of  nitrogen,  60 
Oxygen : 

Absorption  of  o.  in  spontane- 
ous   combustion,   58;    A. 
by  coal,  111 
Consumed     in     breathing,     3 

(See  B.  Apparatus) 
Density,  sp.  gr.,  mol.  wt.,  sym- 
bol, 89 

Depletion  of  o.  in  air,  4; 
Caused  by  absorption  of 
o.  Ill;  Effect  on  flame, 
312;  Effect  on  life,  4; 
Increases  poisonous  ac- 
tion of  carbon  monoxide, 
107 

Normal  percentage  of  o.  in 
air,  4 


428 


INDEX 


Paraffins,  92 

Paul  breathing  apparatus,  147 

Percentage  composition:  By  vol- 
ume,    40;     By    wt.,     39 
Calculation  of  p.  c.  of  air,  30 

Percentage    of   gas   re   height   of 
fame    cap;    Chart;    303 
Calculation  of  h.  of  f.  c., 
304;     Diagram;    Formu- 
las, 305 

Permissible   breathing   apparatus, 
148  (See  B.  A.) 

Permissible   electric  mine  lamps, 
319  (See  E.  M.  L.) 

Permissible    mine    safety    lamps, 
288  (See  L.,  M.  S.) 

Phlogiston,  1 

Physics   of  air  and  gases,  17  (See 
Expansion  of  A.  and  G. ; 
Hygrometry) 
Tension    (pressure)   of  a.,    19 

Pieler  safety  lamp,  282;  Chart  of 
1.  flame,  303 

Plan  of  mine,  General,  252 

Requirements  re  drainage, 
haulage  and  ventilation; 
Economy  and  efficiency; 
Drainage,  252;  Haulage, 
253;  Road  angle  re  grade 
in  inclined  seam;  Formu- 
las, 254;  Distribution  of 
air,  257 

System  of  mining:  Room-and- 
pillar,  254,  255;  Long- 
wall,  256,  257;  Single, 
Double,  Triple-entry  sys- 
tems, 263;  Multiple-entry 
system;  Economy  of  m. 
main  airways,  265 
Output,  Estimation  for  given, 

266 

*   Ventilation  of  longwall  work- 
ings, 256 


Potential  (See  Mine  P.) 

Explanation  of  potential  prin- 
ciple, 196 

Formulas:  P.  of  airway,  200; 
Values,  dif.  a.  (table),  202  ; 
P.  of  circulation,  201 ;  Val- 
ues, dif.  c.  (table),  203 
Pressure  p.;  Power  p. — 
Caution,  207;  Equivalent 
p.  f.;  Power;  Pressure, 
208;  Quantity,  209;  Il- 
lustration 197,  198 
Part  p.  values,  212;  Illus- 
tration, 213,  216 
Relative  p.  values,  221;  Illus- 
tration, 224 

Split  p.  formula,  204;  Ex- 
amples, 205-207,  209; 
Split  power  p.  and  press. 
p.  f.  211;  Ex.;  General 
s.  p.,  229 

Summation  of  split  p.,  232 
Tandem      circulations,      214: 
Summation    of    p.,    214, 
215;  General  t.  p.  form- 
ulas, 216 

Use  of  p.  factors,  208 
Pound :  Unit  of  mass,  25 
Pound -calorie,  52;  Value  of,  53; 

Pound-molecule,  67 
Power  on  the  air,  182  (See  Mine 

Ventilation) 
Power,  volume,  pressure  diagram, 

185 

Practical  ventilation  (See  V.  ,P.) 
Pressure    (See   Mine   Ventilation) 
Effect  of  p.  on  air  and  gas,  17; 
E.    on     freezing,    fusion, 
melting  points,  49;  E.  on 
boiling  point  and  vapori- 
zation, 50 
Heat  due  to  p.,  47 
Power,   volume,   p.    diagram, 

185 

P.  re  absolute  temp.  20 
P.  of  occluded  gas,  35 


INDEX 


429 


Pressure : 

Primary  and  secondary  splits, 
219;  P.  and  s.  pressures, 
239 

Proportionate  division  of  air,  230 
(See  Splitting  the  A. 
Current) 

Regulators  required,  219,  230 
(See  R.) 

Psychrometer,  71  (See  Hygro- 
meter, The) 

Pulmotor,  103 

Q 

Quantity  of  air,  181  (See  Mine 
Ventilation) 

R 

Radiation  of  heat,  52 
Ratios,  Solution  by  (in  mine  ven- 
tilation), 173 
Reaction,  Chemical,  56 

Endothermic;  Exothermic,  65, 

67 

Interchange  of  atoms,  62 
Molecular  heat  of  the  r.,  67 
Regulate  the  air,  To,  230 
Regulators    (in  mine  ventilation), 

239,  251 
Effect  of  r.,  231 
Kind:  Box   r.;   Door  r.,   321 
Pressure  due  to  box  r.,  232; 
Area  of  opening  in  b.  r., 
234;   Example,   240;   Ve- 
locity   and    quantity    of 
air  passing,  233 
Use  of  the  door  r. ;  Area  of 
opening;    Example,    240; 
Quantity  of  air  passing,  235 
Rescue    work  in  mines   (See  Ex- 
plosion, M.) 
Resistance    of   airways,    191    (See 

A.) 

Respiration     (See     Artificial     R.) 
Action  in  r.  wearing  breathing 
apparatus,  133 


Respiration : 

Capacity  of  lungs;  Rate  of 
breathing;  Quantity  of 
air  exhaled  each  breath; 
Quantity  of  air  inhaled 
per  min.  depending  on 
exertion;  Volume  of  car- 
bon dioxide  exhaled  about 
equal  to  vol,  of  oxygen 
inhaled,  133 
Effect  of  carbon  dioxide  on  r., 

109,  110 

Quantity  of  oxygen  consumed 
in  breathing,  3 

Respiratory  action,  3 

Origin  and  regulation  at  nerve 
center;  Transmitted  to 
r.  muscles  produces 
breathing ;  Oxygen  ab- 
sorbed by  the  blood  and 
carried  in  the  circulation 
oxidizes  the  impurities, 
which  are  expelled  largely 
in  the  carbon  dioxide 
of  the  exhaled  breath 
containing  2  or  3  per 
cent,  of  that  gas,  3 

Respiratory  system,  2 

Purpose  to  oxidize  the  organic 
matter  of  the  body  and 
accomplish  its  removal  in 
form  of  carbon  dioxide 
in  the  exhaled  breath. 


Safety  lamps,   Mine   (See  L.,    M. 

S.) 

Salts,  in  chemistry,  61 
Saturation  of  air  (See  Hygrometry) 
Scale  of  air,  in  ventilation,  260 
Secondary  splitting,  235 

Diagram  of  s.   s.;  Formulas, 

general  split  potential  and 

gen.     tandem     potential; 

Illustration  of  s.  s.,  236; 


430 


INDEX 


Examples,  237-239;  Pri- 
mary and  s.  pressure,  239 ; 
Symbols,  236 

Secondary  splits,  Primary  and,  219 

Shaft  columns,  in  ventilation,  168 
(See  Air  C.) 

Slope  mines,  Natural  ventilation 
in,  162 

Shaw  gas  machine,  297 

Single -entry  system,  in  ventila- 
tion, 263 

Solids,  23;  Conduction  of  heat  in 
s.,  52;  Standard  for  s., 
31 

Solution,  Solvent,  48 

Specific,  Meaning  of  the  term : 
S.  gravity;  S.  heat; 
S.  volume;  S.  weight; 
Relative  measurements 
referred  to  adopted 
standards,  28 

Specific  gravity,  30 

Definition;  General  formula, 
30;  S.  g.  of  substances 
(table),  32;  Finding  s.  g. 
of  gases,  liquids;  solids — 
formulas,  31;  Use  of  s.  g., 
33;  S.  g.  of  mixed  gases; 
Calculation,  40;  S.  g. 
caluclated  by  law  of  dif- 
fusion; Formula,  41;  S.  g. 
of  mine  gases  (table),  89 

Specific  heat,  54 

S.  h.  per  gram-molecule  is 
molecular  h.,  47;  S.  h.  of 
a  substance  is  its  relative 
h.  capacity,  54;  S.  h.  of 
solids,  liquids,,  gases 
(tables),  55;  S.  h.  varies 
with  temp.,  56 

Specific  measurement:  Elements 
the  basis  of  relative  m., 
30;  Relative  m.  shown  by 
chemical  equation  giving 
mol.  wts.  and  vol's.,  63; 
Rel.  vol.  of  a  gaseous 


atom     the     unit  of  vol., 

63,  64;  Relative  humidity 

of  air  expressed  by  ratio 

of  actual  vapor  pressure 

to  the  saturated  v.  p.,  74 

Specific  volume   (See  Atomic  V.) 

Specific  weight  (See  Atomic  W.) 

Specifications,      by      Bureau      of 

Mines: 

Permissible  breathing  appa- 
ratus, 148  (See  B.  A.);  P. 
electric  mine  lamps,  319 
(See  E.  M.  L.);  P.  mine 
safety  lamps,  288  (See 
L.,  M.  S.) 
Splitting  the  air  current,  218,  260 

A.  splits,  258 

Effect  of  s.  on  mine  potential, 
203;  E.  on  mine  resist- 
ance, 245;  E.  on  quan- 
tity, 245;  E.  on  velocity, 
244 

Equal  splits;  Illustration,  223; 
General  mine  potential, 
213;  Ex.,  214 

Formulas  Split  potential,  204; 
S.  power  and  s  press,  pot., 
211;  General  tandem 
power  and  press,  pot's. 
216;  Summation  of  split 
pot.,  222;  Sum.  of  pot's 
in  secondary  s.,  237; 
Advantage  in  sum.  of 
pot.  values,  227 

Natural  division  of  a.,  220 
Ex.,  224,  225-230;  N.  s.; 
Proportionate  s.,  219 

Need  of  s.  the  a.  c.,  218; 
Method  of  s.,  219 

Practical  conditions,  result 
of  s.,  243;  Ex.,  245 

Primary  and  secondary  splits, 
219 

Proportionate  division  of  a., 
230  (See  Regulators); 
Ex.,  232 


INDEX 


431 


Splitting  the  air  current : 

Quantity,    Increase    of,    219; 
Q.  proportional  to  num- 
ber of  splits,  243 
Theoretical  considerations  in 

8.,  242 

Unequal  splits,  illustrated,  224 
Spontaneous  combustion,  58 
Cause  of  explosion,  127 
Standards,  Comparison  of,  30 

Air,   hydrogen,    water   30,    31 
S.  for  gases;  S.  for  liquids 
and  solids,  31 
Static  force,  25 
Steam,  82 

Definition ;   Saturated  s. ;  Su- 
perheated s.,  82 
Diagram   of  heat   and  temp. 

curves,  83 

Steam     tables     (Marks     and 
Davis),  by  permission  of 
publishers,        Longmans, 
Green  &  Co.,  84,  85 
Stone  Dust  (See  D.,  Shale  or  s.) 
Stoppings,  in  mine  ventilation,  249 
Stokes  alcohol  lamp,  284 
Sulphuric  acid,  61 
Symbol,  Chemical,  58 
S.  of  a  molecule,  58 
S's  in  mine  ventilation,    192 


Tables: 

Circumferences  and   areas   of 

circles,  391 
Conversion  of  compound  units, 

411;    Conversion  t.; 

Weights    and    measures, 

U.  S.  and  metric,  407 
Logarithms   of  numbers,    333 
Sines  and  cosins,  353 
Squares,    cubes,    s.    roots,    c. 

roots   and   reciprocals   of 

numbers,  373 
Tangents  and  cotangents,  363 


Tandem     circulations,     214     (See 
C.  in  mines) 

Temperature,  43 

Absolute  t.  Rel.  to  vol.  of 
air  and  gas,  18;  Rel.  to 
press,  of  air  and  gas;  T., 
press.,  vol.  of  air  and 
gas,  20;  Abs.  zero,  18; 
How  t.  is  measured-two 
scales,  43;  Table,  Fahr. 
and  centigrade  scales,  44 
Mean  observed  t.  dif.  alti- 
tudes (table),  11;  Drop 
in  t.  as  altidude  increases 
above  sea  level  (table), 
12;  Rel.  of  drop  in  t.  to 
alt.  (formula),  13;  Aver- 
age t.  of  atmos.  air  col- 
umn (formula,)  14 
Volume  of  air  and  gas,  Effect 
of  t.,  17 

Temperature    of    flame     (see    F., 
Nature  and  T.  of) 

Temperature  of  ignition,  117 

Table  of  t.  of  i.  of  gases, 
117 

Testing  for  gas,  295   (See  Flame 

Caps) 

Making  a  test  for  gas  in  the 
mine,  306;  Use  of  gas  in- 
dicators (See  G.  1.);  Use 
of  lamps  in  t.  for  g,  (See 
L.,  Mine  Safety) 

Theory    of    ventilation,    161    (See 
Mine  V.) 

Thermal  units,  51  (See  Heat) 

Thermochemistry,  65 

Writing  a  thermochemical 
equation,  67,  69 

Thermometer  scales,  43 

Comparison  of  Fahr.  and 
centigrade  s.  (table)  44 

Time  in  estimation  of  velocity  and 

power,  26 

Calendar  t. — Day:  Solar  d., 
Sidereal  d.;  Month;  Year: 


432 


INDEX 


Solar  y. ;  Sidereal  y. ;  Com- 
mon y.  ;Leap  y.,  401 
Measurement  of  t. :  Sun  t. ; 
Sidereal  t. ;  Equation  of  t., 
Local  t.,  Standard  t.,  402; 
Eastern  t.,  Central  t., 
Mountain  t.;  Pacific  t. ; 
Civil  t.,  Astronomical  t., 
403 

Transmission  of  heat,  52  (See  H.) 
Transpiration  of  Gases  from  Coal, 

35 
Relative  velocity  of  t.  (table), 

35 
Triple-entry  system,  263 

U 

Undercast,  in  mine  ventilation, 
249,  251 

Units  of  measurement:  Special  u.; 
Compound  u.;  U.  veloc- 
ity; U,  work;  U.  power, 
26,  406;  Heat  u.,  51; 
Kinds  of  u.,  397;  U.  of 
ventilating  press.,  177; 
U.  resistance,  192 


Valence,  valency,  59 
Vaporization,    Evaporation,    Boil- 
ing, 50 

Effect    of   press,    on    v.,    50; 

B.  points  of  liquids  (table; 

51;  V.  takes  place  at  all 

temp.,  24,  80 
Vapors  and  Gases,  24  (See  Hygrom- 

etry) 

Definition  of  a  v.,  24 
Laws  of  v.,  80 
Saturated    v.    press,    (table), 

77 
V.  saturates  space  it  occupies, 

80 
Wt.    of    water   v.;    formulas, 

79,  80;  Diagram,  81 


Velocity   (See   Air  Currents,  Con- 
ducting) 
Constant  v.,  25;  Acceleration, 

26 
Ventilating     pressure,     174     (See 

Mine  Ventilation) 
Ventilation,    Mine    (See    M.    V.) 
Ventilation,    Practical,    248     (See 
Air  Currents,  Conducting) 
Distribution  of  air,   257   (See 
Splitting  the  Air  Current) 
Entry  systems :  Single,  Double, 
Triple,  263;  Multiple,  e.  s., 
265; 

V.    of    cross-entries,    259;    V. 
of  mine  stables,  260;  V.  of 
longwall  workings,  256 
Natural  v.  in  slope  and    dip 

workings,  162 

Plan  of  mine  (See  P.  of  M.) 
Systems  of  V.  (see    Mine  V.) ; 

S.  of  mine  airways,  262 
Volume:     Atomic    or   specific    v; 
Molecular  v. ;  Avogadro's 
law  of  v.,  29;  Application 
of    1.    of   v.,    64;    V.    of 
atom,  unity,  64 
Density  and  v.,  29 
Mass,  v.,  density,  24 
V.  re  abs.  press.,  19;  re 

abs.  temp.,  18 
V.,  press.,  temp.,  20 
Power,  v.,  press,  diagram,  185 
Volatile  oil  flame,  sensitive  to  gas, 

288 
Volatile  oils,  in  safety  lamps,  (See 

Ilium  inants  for  S.  L.) 
Give  fuel  cap  in  testing  for 

gas,  271 
Light  v.  o.,  308 


Water:  Density  referred  to  air, 
31;  Unit  wt.  dif.  temp, 
(table),  34 


INDEX 


433 


Water  column,  Calculation  of,  6 
Water  gage,  The  Mine,  175 

Calculation  from  m.  potential, 

206 
Equivalents  in  measurement, 

175,  185;  Diagram,  184 
Reading  the  w.  g.,  177 
Scales,  Dif.,  176 
Use  of  w.  g.  in  the  mine;  What 

it  shows,  178 
Water    vapor     (See    Vapors    and 

Gases) 
Weight : 

A  property  of  matter,  22 
Atomic  w.,  molecular  w.,  59 
W.  of  air:  Formulas,  4,  79,  80; 

Dif.  altitudes  and  temp. 

(tables),     11,    15;    W.  of 

elements  (table),  28;  W.  of 

substances  (table),  32;  W. 

of  water,  dif.  temp.,  31, 33; 

W.of  oils  (table),  33;  W. 

of  woods  (table)  34 
Weights  and  measures,  397 

Systems  in  use;  Standards  of 

weight,  length,  capacity, 

397 


Weights  and  measures: 

U.  S.  and  British  systems,  398 
Calendar  time,  401 
Measurement  of  time,  402 
Metric  system  of  w.  and  m., 
403;      Metric     abbrevia- 
tions,   406 ;      Conversion 
tables,    406;    Compound 
units,  411 
Wet-and-dry  bulb  hygrometer,  72 

(See  H.) 

Whitedamp  (See  Carbon  Monoxide) 
Wire  gauze :  Cooling  effect ;  Prin- 
ciple of  w.  g.,   Standard 
mesh,  269 
Windy  shot,  in  blasting,  cause  of 

explosion,  127 

Wolf  safety  lamp,  285 ;  Flame- 
cap  diagram,  303 
Wood,  Wt.,  of  dif.,  (table),  34 
Work: 

Internal  w.  due  to  expansion 
of  air  or  gas,  calculated 
in  two  ways,  20,  21 
W.,  in  mine  ventilation,  syn- 
onymous with  "power  on 
the  air,"  182 


YC  33742 


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